Length of Side of cube - shaped storage container is 2 units .
Given : Volume of container = 8 cubic units .
To find : the length of one side of the container .
Formula for volume of cube : Volume of cube = [tex]x^{3}[/tex] .
According to ques .
[tex]x^{3}[/tex] = 8
Solving cubic equation ,
finding cube root of 8 and hence finding value of x .
[tex]\sqrt[3]{8}[/tex] = x
x = 2
2 * 2 * 2 = 8 .
Hence , length of each side of cube - shaped storage container = 2 units .
To learn more on volume of cube :
https://brainly.com/question/19891526
#SPJ9
Explain a strategy you use to identify a pattern.
A good way to find patterns in data is to arrange it in tabular form, which acts as an "input-output" machine.
What strategy do you use to identify a pattern?A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements. Any kind of event or object can be connected to the Pattern.
A pattern is referred to as a rule or a way in which a group of numbers is related to one another. Sometimes a pattern is also referred to as a sequence.
Putting data into a tabular format, which functions as an "input-output" computer, is a useful way to find patterns. It will process an input value, return an output value, and take another value as an input.
The table's process column will make it easier to comprehend how input and output are related.
To learn more about patterns, refer to:
https://brainly.com/question/24160693
#SPJ4
8) Sam's test score is between 100 and 107. His friend Tammy scored about 15 less points.
Part A
Write a compound inequality that describes Tammy's test score x.
Part B
How much did Tammy score?
The compound inequality that describes Tammy's test score x 85 < x < 92 and Tammy's test score is between 85 and 92
Part A: Write a compound inequality that describes Tammy's test score x.The given parameters are
Sam's test score is between 100 and 107
This means that
100 < Sam's score < 107
From the question, we have:
Tammy scored about 15 fewer points.
This means that
Tammy = Sam - 15
So, we have
Sam = Tammy + 15
Where
Tammy = x
This gives
Sam = x + 15
So, we have
100 < x + 15 < 107
Subtract 15 from the sides of the inequality
So, we have
85 < x < 92
This means that the compound inequality that describes Tammy's test score x 85 < x < 92
Part B: How much did Tammy score?In part (a) of this solution, we have the following compound inequality
85 < x < 92
The above compound inequality means that Tammy's test score is between 85 and 92
Read more about inequality at
https://brainly.com/question/24372553
#SPJ1
According to your company's safety regulations, the distance from the base of a ladder to a wall that it leans against should be at least one fourth of the ladder's total length. You are given a 20 -foot ladder to place against a wall at a job site. If you follow the company's safety regulations, what is the maximum distance x up the wall the ladder will reach, to the nearest tenth?
F 12 feet
G 19.4 feet
H 20.6 feet
J 30.6 feet
The maximum distance up the wall the ladder will reach = 19.4 ft
The total length of the ladder, L = 20 ft
Minimum distance of the base of the ladder to the wall, B = 1/4 x 20 = 5 ft
Now we need to find the maximum distance up the wall the ladder will reach. This is obtained when the base distance is the least.
i.e., when the base = 5 ft.
Now the ladder, the wall and the base distance between wall and ladder constitute a right triangle. In this right triangle, the ladder is the hypotenuse and the height of the wall up to which ladder reach, 'x' is its altitude with base = 5ft.
Then using Pythagoras theorem,
[tex]L^2 = B^2 +x^2[/tex]
⇒ [tex]x^2 = L^2 - B^2 = 20^2 - 5 ^2[/tex]
⇒ [tex]x^2 = 375[/tex]
⇒ [tex]x=\sqrt{375}[/tex] = 19.3649
When rounded to the nearest tenth, (i.e., only one decimal place),we get,
⇒ x = 19.4 ft
Learn more about Pythagoras theorem at https://brainly.com/question/21970437
#SPJ4
Write the equation of the line that passes through (5, −2) and is perpendicular to y equals 5 thirds times x minus 3 period
Answer:
5y =x-15
Step-by-step explanation:
yes
The equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The line passes through (5, −2) and is perpendicular to y = (5/3)x - 3
The slope of the line y = (5/3)x - 3
m = 5/3
The slope of the line perpendicular to the above line:
M = -3/5
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
The equation of the line
y + 2 = (-3/5)[x - 5]
y = -3x/5 + 1
Thus, the equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ5
Express 48 as sum of two odd prime
Answer:
19 , 29
Step-by-step explanation:
19 + 29 = 48
mark brainiest pls
Solve the inequality.
x+13<41
For the given inequality x+13<41, x is less than 28
Inequality involves two algebraic expressions linked by the signs of inequality. These signs include less than (<), greater than (>) or less than equal to (<=) and greater than equal to (>=).
Let's solve the inequality
x+13<41
Move the like terms on the same side
x< 41-13
x< 28
Therefore, x is less than 28
You can learn more about inequalities from
https://brainly.com/question/11613554
#SPJ4
Find the geometric mean between pair of numbers.
7 and 11
The geometric mean between pair of numbers 7 and 11 is 8.77
We know that for a sequence of numbers x1, x2,.., xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers 7 and 11
We need to find the geometric mean between pair of numbers, 7 and 11.
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{7\times 11}\\\\ \Pi=\sqrt{77}\\\\ \Pi=8.77[/tex]
Therefore, the geometric mean between pair of numbers 7 and 11 is 8.77
Learn more about the geometric mean here:
brainly.com/question/8934175
#SPJ4
Write an equation of a parabola with the given information.
vertex (3,2) , focus (4,2)
The equation that defines the parabola with vertex at the point (3, 2) and focus at (4, 2) is:
(Y - 2)² = 16(X - 3)
A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)(y - k)² = 4p(x - h)This will depend on its aperture
In this case we have the vertex of the parabola at the point (3, 2) and the focus at the point (4, 2) this is displaced on the x-axis to the right, so the parabola is of the form X = Y²
(y - 2)² = 4p(x - 3)
Focus
f = (0 + p, 0)
0 + p = 4p = 0 + 4p= 4(y - 2)² = 4*4(x - 3)
(Y - 2)² = 16(X - 3)
Y² - 4Y + 4 = 16X - 48
X = Y²/16 - Y/4 + 13/4
Learn more about parabolas in:
https://brainly.com/question/28586996
#SPJ4
100 POINTS! ANSWER PLEASE! Order the following rational and irrational numbers from least to greatest. -2 3/5, square root of 20, 3.9, 10/3, 3 7/8
The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
What is the arrangement of the numbers in ascending order?It follows from the task content that the numbers given are rational and irrational numbers.
To order the numbers, they should be converted to decimal numbers as follows;
-2 3/5 = -2.6√20 = 4.473.9 = 3.910/3 = 3.333 7/8 = 3.875Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
Read more on ascending order;
https://brainly.com/question/12783355
#SPJ1
The circle below is centred at O.
a) Work out the size of angle x.
b) Which of the circle theorems below allows
you to calculate this angle?
x
27°
Not drawn accurately
The angle at the circumference in a semicircle is a right angle
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between the tangent and the radius at a point
on a circle is 90°
The perpendicular line from the centre of a circle to a chord
bisects the chord
Two tangents that meet at a point are the same length
Answer:
[tex]\textsf{a)} \quad x = 63^{\circ}[/tex]
[tex]\textsf{b)} \quad \boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Step-by-step explanation:
Part (a)The triangle inside the circle is an isosceles triangle, since two of its sides are the radius of the the circle (and therefore equal in length).
Therefore, its two base angles are 27°.
A tangent is a straight line that touches a circle at only one point.
The tangent of a circle is always perpendicular to the radius.
[tex]\implies x + 27^{\circ} = 90^{\circ}[/tex]
[tex]\implies x +27^{\circ}-27^{\circ}= 90^{\circ} - 27^{\circ}[/tex]
[tex]\implies x = 63^{\circ}[/tex]
Part (b)The circle theorem that allows the calculation of angle x is:
[tex]\boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Find the sum of each series. Σ¹° n=4 (0.8 n-0.4)
The given series is an arithmetic series and its sum is 36.4
The summation or sigma notation is used to express long summation into a single formula.
The series, given in a summation notation, is:
[tex]\sum\limits^{10}_{n=4} {(0.8n-0.4)}[/tex]
The formula inside the sum notation represent the nth term, a(n).
Let evaluate the terms for some n, starts from n = 4 as indicated by the lower limit of the summation notation:
a(4) = 0.8 (4) - 0.4 = 2.8
a(5) = 0.8 (5) - 0.4 = 3.6
a(6) = 0.8 (6) - 0.4 = 4.4
This form a new arithmetic series, with the first term, let say f(1) =2.8 and common difference, d = 0.8.
The number of terms in this new geometric series is given by the upper and lower limit of the summation notation:
number of terms = 10 - 4 + 1 = 7
Use the sum formula for an arithmetic series,
S(n) = n/2 [2.f(1) + (n - 1) . d]
Substitute n = 7, f(1) = 2.8, and d = 0.8 into the formula:
S(7) = 7/2 [2. (2.8) + (7 - 1) . (0.8)]
S(7) = 36.4
Learn more about series here:
https://brainly.com/question/18304639
#SPJ4
Evaluate -8 × |2|.
-16
-10
16
10
Answer:
[tex] - 8 \times |2 = - 16| [/tex]
what is cube root of 16 as a power of 2?
Answer: The prime factorization of 16 is 2 × 2 × 2 × 2, hence, the cube root of 16 in its lowest radical form is expressed as 2 ∛2.
Cube Root of 16.
Step-by-step explanation:
The solution for the cube root of 16 as a power of 2 is,
⇒ ∛16 = 2 ∛2
We have to given that,
To find the cube root of 16 as a power of 2.
The prime factorization of 16 are,
16 = 2 x 2 x 2 x 2
Take cube root,
⇒ ∛16 = ∛2 x 2 x 2 x 2
⇒ ∛16 = 2 ∛2
Therefore, The solution for the cube root of 16 as a power of 2 is,
⇒ ∛16 = 2 ∛2
Learn more about the factors visit:
https://brainly.com/question/219464
#SPJ6
Write an equation of the line through each pair of points in slope-intercept form.
(-12,-6) and (8,9)
The equation of line is:
y = (5/2) x - 11
Given,
Points (x₁, y₁) = (-12, -6) and (x₂, y₂) = (8, 9)
We can find the slope using the equation for slope
m = (y₂ - y₁) / (x₂ - x₁)
= (9 -(-6)) / (8-(-12))
= (9+6) / (8 + 12)
= 15/20 = 3/4
We know the slope and a point, so we can use point slope form to make an equation
y-y₁ = m(x-x₁)
y - (-6) = 3/4 (x-(-12))
Distribute
y+6 = 3/4x – 3/4 × 2
y+6 = 3/4x - 3/2
Add -6 to each side
y + 6 -6 = 3/4x - (3/2)-6
y = 3/4x - (-9/2)
y = 3/4x + 9/2
This is in slope intercept form (y= mx+b)
Learn more about slope intercept here: brainly.com/question/12097185
#SPJ4
What is the measure of 24 in the triangle shown?
32°
117°
22
148
The sum of three angles of a triangle is 180° . 32° is the angle at 24 when other two angles are 85° and 63°.
What is angle sum property?The sum of three angles of a triangle is 180° .
Given two angles of a triangle are 85° and 63°. We need to find the third angle at 24.
The angle at 24 be x.
By angle sum property,sum of three angles of a triangle is 180°.
The two angles are 85° and 63° and third angle is x.
85°+63°+x=180°
148°+x=180°
x=180°-148°
x=32°
Therefore the angle at 24 is 32° when other two angles are 85° and 63°.
To learn more on Angle sum property click:https://brainly.com/question/21067919
#SPJ1
A triangle has side lengths of (8w + 8x) (8w+8x) centimeters, (3w + 10y) (3w+10y) centimeters, and (4y + 8x) (4y+8x) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
The expression that represents the perimeter of the triangle in centimeters is; 73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex] + 60wy + 116[tex]y^{2}[/tex] + 64xy
We are given the measurement of each side length of the triangle, i.e.
(8w +8x) (8w+8x)
(3w + 10y) (3w+10y)
(4y + 8x) (4y+8x)
After simplifying the measurement on each side, we get;
(8w +8x) (8w+8x)= 64[tex]w^{2}[/tex] + 128wx + 64[tex]x^{2}[/tex]
(3w + 10y) (3w+10y)= 9[tex]w^{2}[/tex] +60wy +100[tex]y^{2}[/tex]
(4y + 8x) (4y+8x)= 16[tex]y^{2}[/tex] + 64xy + 64[tex]x^{2}[/tex]
To find the perimeter of the triangle, we get the addition of all side lengths
Thus, Perimeter (P) = 64[tex]w^{2}[/tex] + 128wx + 64[tex]x^{2}[/tex] + 9[tex]w^{2}[/tex] +60wy +100[tex]y^{2}[/tex] + 16[tex]y^{2}[/tex] + 64xy + 64[tex]x^{2}[/tex]
P= 73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex] + 60wy + 116[tex]y^{2}[/tex] + 64xy
Therefore, the perimeter of the triangle is given by; 73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex] + 60wy + 116[tex]y^{2}[/tex] + 64xy
To find more on perimeter, use; brainly.com/question/10971545
#SPJ4
simplify x+2/x^2+2x-3/x+2/x^2-x
if g(x)=3x+7 what is g(4b) show your thinking
Answer: g(4b)=12b+7
Step-by-step explanation:
g(x)=3x+7
g(4b)=3(4b)+7
g(4b)=12b+7
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
Answer:
x = 5
Step-by-step explanation:
3(x + 7) + 4 = 40 ( subtract 4 from both sides )
3(x + 7) = 36 ( divide both sides by 3 )
x + 7 = 12 ( subtract 7 from both sides )
x = 5
As a check
substitute x = 5 into the left side of the equation and if the value obtained is equal to the right side (40) then it is a solution
3(5 + 7) + 4
= 3(12) + 4
= 36 + 4
= 40
left side = right side
then x = 5 is the solution to the equation
PLEASE HELP WILL MARK BRAINLIEST !!
Answer: y=-0.5x-8
Step-by-step explanation:
Choose two points on the line: (0,-8) and (-6,-5)
Hence,
x₁=0 x₂=-6 y₁=-8 y₂=-5
[tex]\displaystyle\\The\ slope=\frac{y_2-y_1}{x_2-x_1}\\\\The\ slope=\frac{-5-(-8)}{-6-0} \\\\The\ slope=\frac{-5+8}{-6} \\\\The\ slope=\frac{3}{(3)(-2)}\\\\The\ slope=\frac{1}{-2} \\\\The\ slope=-\frac{1}{2}\\\\The\ slope=-0.5[/tex]
[tex]y=kx+b\\k=the\ slope=-0.5\\(0,-8) \ hence,\\-8=-0,5*0+b\\-8=0+b\\-8=b\\Thus,\\y=-0.5x-8[/tex]
Determine whether the polygons are always, sometimes, or never similar. Explain your reasoning. (Lesson 7-2).
An equilateral triangle and a scalene triangle
The given polygons that is an equilateral triangle and scalene triangle can never be similar ,as it is not possible to map equilateral triangle onto scalene triangle or vice-versa.
As given in question,
Given polygons are equilateral triangle and scalene triangle
An equilateral triangle never similar to scalene triangle.
Reason:
All sides of equilateral triangle are equal where as all sides of scalene triangle are not equal.Using transformation dilations and rigid it is not possible to map equilateral triangle onto scalene triangle or vice-versa.Therefore, the given polygons that is equilateral triangle and scalene triangle can never be similar.
The complete question is:
Determine whether the given polygons are always, sometimes, or never similar. Explain your reasoning.
An equilateral triangle and a scalene triangle
Learn more about polygons here
brainly.com/question/24464711
#SPJ4
Sherry mccoy is a tax consultant. she charges $425 per diem for her services. if she worked 180 days last year, what was her gross income for the year?
With a rate of $425/day, Sherry McCoy's gross income for the year, working 180 days, is $76,500.
Gross income refers to the total salary or wages and other form of earnings before any deductions or taxes.
If as a tax consultant, Sherry McCoy charges $425 per diem for her services, then her rate is $425/day.
Rate is a ratio that compares two different quantities which have different units.
We will use this rate to find how much earnings she got if she worked for 180 days last year.
gross income = rate x time
gross income = $425/day (180 days)
gross income = $76,500
Hence, working 180 days last year, Mary has a gross income of $76,500.
Learn more about gross income here: https://brainly.com/question/13793671
#SPJ4
If x varies partly as y and partly as the square of y when y =2,x=5 bad when y=5,x=57.5 find x when y =4
The value of x when y = 4 is 0. 25
How to determine the valueFrom the information given, we have that;
x varies directly as yx also varies partly as y²This is expressed as;
x ∝ 1/ y²
x = y/y²
Let's substitute the value of y as 4 into the equation;
x = 4 / 4²
Find the square
x = 4 / 16
Find the ratio
x = 1/ 4
x = 0. 25
Thus, the value of x when y = 4 is 0. 25
Learn more about variation here:
https://brainly.com/question/6499629
#SPJ1
4)
What would be the actual length, if the length of the model is 10 ft and the scale factor is greater
than one?
a) 10 ft
(b) 9.5 ft
c) 4yd
The actual length, if the length of the model is 10 ft and the scale factor is greater than one is Option(b) 9.5 ft.
What is Scale-Factor?Any geometric figure or object's size can be changed with respect to its original size by applying a scale factor, which is a numerical value. It is used to find the length, area, or volume that is missing from an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined.The image is magnified if the scaling factor (k > 1) is greater than 1.The image is shrunk if the scale factor is less than 1 (0 < k <1).The image doesn't change if the scaling factor is 1 (k = 1).There cannot be a zero scale factor.The basic formula to find the scale factor of a figure is as:
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given:
length of the model = 10 ft
Now we determine which actual length has a scale factor greater than one.
(a) Scale factor = (10/10)
Here, we can see that the scale factor is equal to 1.
(b) Scale factor = (10/9.5) = 1.05
Here, we can see that the scale factor is greater than 1.
(c) Scale factor = (10/12) = 0.83 ( 1 yard = 3 foot)
Here, we can see that the scale factor is less than 1.
Therefore, the actual length is 9.5 ft.
To know more about the scale factor visit:
https://brainly.com/question/17838614
#SPJ9
Is the relation a function… yes or no?
Answer: Functions are relations with one output for any unique input.
Step-by-step explanation:
What is the value?
90.5=
1/81
4.5
3
Answer:181/2
Step-by-step explanation:
90.5 as a fraction is 181/2
Write an equation in slopeintercept form that describes the line containing the points (-1,0) and (2,4) .
The equation in slope-intercept form y = 4/3 x + 4/3 contains the points (-1 , 0) and (2 , 4).
An equation of a line in slope-intercept form is given by the formula y = mx+ b, where m is the slope of the line and b is the y- intercept.
If you know two points on a line, you can use them to write the equation of the line in slope-intercept form.
First is to find the slope of the line using the two given points.
let Point 1(-1 , 0) and Point 2(2 , 4)
slope = m = (y2 - y1) / (x2 -x1)
m = (4 - 0) / (2 - -1)
m = 4/3
Next, use the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = 4/3 x + b
Using Point 1,
0 = 4/3 (-1) + b
0 = -4/3 + b
b = 4/3
Finally, set up the equation of the line in slope-intercept form.
y = mx+ b
where m = 4/3 and b = 4/3
y = 4/3 x + 4/3
To learn more about equation in slope-intercept form: https://brainly.com/question/25826868
#SPJ4
URGENT HELP PLEASE!!! In the figure below, FG=6 and GH=8. Find FH.
Answer:
14
Step-by-step explanation:
Adding FG and GH is the answer to the wholr line. Im 90% sure thats the right answer thats whst i learnt 7 days ago.
Find the coordinates of the midpoint of a segment with the given endpoints. A(13,14), C(3,5)
The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(13, 14) and C(3, 5).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(13 + 3) / 2, (14 + 5) / 2]
(x, y) = (16/2, 19/2)
(x, y) = (8, 9.5)
The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).
More about the mid-point of the line segment link is given below.
brainly.com/question/17188072
#SPJ4
I WILL GIVE U EXTRA BRAINLY POINTS!!
i don't understand this please help :)
Two angles are supplementary is the measure of one angle is 54.3 degrees what is the measure of the other angle? Answer to the first decimal place, ie 79.5.
Answer: 125.7 degrees
Step-by-step explanation:
supplementary angles add up to 180 degrees.
angle 1 + angle 2 = 180
54.3+angle 2=180.0
54.3-54.3+angle 2=180.0-54.3
angle 2=180.0-54.3
angle 2=125.7 degrees
