6x + 8 < 3x + 4
6x - 3x < 4 - 8
3x < -4
x < - 4/3
Answer:
-4/3
Step-by-step explanation:
A box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many square inches of paper are needed?
The total surface area of the triangular prism that has a height of h and the side length of a is given below.
[tex]\rm a(\dfrac{\sqrt3}{2} \ a + 3h)[/tex]
What is a triangular prism?A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.
A box is in the shape of an equilateral triangular prism.
If the box is to be covered with paper on its lateral sides.
Let a be the side length of the equilateral triangle and h be the height of the prism.
Then the surface area of the triangular prism will be
Surface area = 2 × area of triangle + 3 × area of the rectangle
The area of the triangle will be
[tex]\rm Area\ of\ triangle = \dfrac{\sqrt{3}a^2}{4}[/tex]
The area of the rectangle will be
[tex]\rm Area \ of \ rectangle = a \ h[/tex]
Then the total surface area will be
[tex]\rm Surface\ area = 2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area = a(\dfrac{\sqrt3}{2} \ a + 3h)[/tex]
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Answer:
72 square inches
Step-by-step explanation:
Find the solution of the system of equations.
x+2y=9
-6x+4y=-46
Answer:
x=-3.5 and y=6.25
Step-by-step explanation:
x+2y=9
x=9-2y
-6(9-2y)+4y=46
-54+12y+4y=46
16y-54=46
16y = 100
y = 100/16 = 50/8 = 25/4 = 6.25
x+2(6.25)=9
x+12.5=9
x= -3.5
Which expression represents the correct form for the quotient and remainder, written as partial fractions, of StartFraction 7 x squared minus 40 x + 52 Over x squared minus 6 x + 9 EndFraction?
Answer:
[tex]A + \frac{B}{x-3} + \frac{C}{(x-3)^{2} }[/tex]
Step-by-step explanation:
First, because the degree of the numerator is the same as the degree of the denominator, this fraction needs simplified further by long division. Upon simplification, the rational expression is [tex]7+\frac{2x-11}{x^2-6x+9}[/tex].
Next, the denominatior needs factored in order to split up the second part of the simplified expression into two different partial fractions. Such factorization yields us, [tex](x-3)^{2}[/tex].
Finally, we have all of our necessary information to set up all of our partial fractions.
This gives us [tex]A + \frac{B}{x-3} + \frac{C}{(x-3)^{2} }[/tex], which is our answer.
A farmer plans to build the small silo shown to store chicken feed. What is the circumference of the base of the silo if it can hold a maximum of 132 cubic feet of feed?
The circumference of the base of the silo that can hold a maximum of 132 cubic feet of feed is approximately 28.796 feet.
How to determine the circumference of the base of a silo
The circumference is the measure of the contour of a circle. In this question we have to determine the radio of the base of the cone from the volume formula and later the circumference is found by this finding:
Volume
V = (π/3) · R² · h (1)
Circumference
s = 2π · R (2)
Where:
R - Radius of the base, in feeth - Height of the silo, in feetIf we know that V = 132 ft³, h = 6 ft, then the circumference that can hold the given capacity is:
[tex]R = \sqrt{\frac{3\cdot V}{\pi \cdot h} }[/tex]
[tex]R = \sqrt{\frac{3\cdot (132\,ft^{3})}{\pi\cdot (6\,ft)} }[/tex]
R ≈ 4.583 ft
s = 2π · (4.583 ft)
s ≈ 28.796 ft
The circumference of the base of the silo that can hold a maximum of 132 cubic feet of feed is approximately 28.796 feet. [tex]\blacksquare[/tex]
RemarkThe statement is complete, complete form is introduced below:
A farmer plans to buid the small silo to store chicken feed. The silo is a cone with a height of 6 feet. What is the circumference of the base of the silo if it can hold a maximum of 132 cubic feet of feed?
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Write an equation of the line that passes through (0, 0) and (2, 6).
Answer:
y=3x
Step-by-step explanation:
hello :
an equation is : y=ax ( the line that passes through (0, 0) )
and (2, 6): x= 2 y=6 qo : 6 = a ×2 a =3
an equation of the line that passes through (0, 0) and (2, 6) is : y=3x
The equation of the line passing through the points (0, 0) and (2, 6) is:
y = 3x.
What is the equation of a line?The equation of a line is a relation between the dependent variable y and an independent variable x, used to determine the value of y for a given x. The general form of such an equation is,
y = mx + b, where m is the slope and b the y-intercept.
What is the two-point formula?The two-point formula is the formula used to determine the equation of a straight line when the slope m and the y-intercept b are not given, but we know two points on the line.
The formula is such: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁).
How do we solve the given question?We have been given two points on the required line, (0, 0) and (2, 6)
We take the points as (x₁, y₁), and (x₂, y₂) respectively.
∴ x₁ = 0, x₂ = 2, y₁ = 0, y₂ = 6.
Since it's an equation of a line, we use the two-point method to determine the equation.
The two-point formula is:
y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
Substituting the values we have, we get:
y - 0 = ((6-0)/(2-0))*(x-0)
or, y = 3x.
∴ The equation of the line passing through the points (0, 0) and (2, 6) is:
y = 3x.
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Barry earns $1300 a month. He spends 30% of this money on rent and 2/7 on bills. How much of the $1300 does he have left?
Answer:
It should be $538 left after the bills
how do i get my math grade up
Answer:
just practice alot . .. ...........
Answer:
you could do all your work and try to ask the teacher for help
Step-by-step explanation:
A group of friends were working on a student film that had a budget of $1200. They used 62% of their budget on props. How much money did they spend on props?
Answer: $804
Step-by-step explanation: 1. Set the equation to x/1200=67/100 2. Cross-multiply so you get 100x=80,400 3. Now divide both sides by 100 to get x=804 which is your final answer 4. Put the dollar sign in front to denote units.
To get your car repaired at a certain dealership in Woodstock, the rate charged is $90 per hour worked on your car, plus a $50 diagnostic fee.
1) Create an equation to find the (C)harge to fix the car:
2) If your car was worked on for 4.6 hours what would be the total charge?
3) If the total cost was $800, how many hours was the car in the shop?
Jake is saving for a new tablet. It costs $250, and he has $100. He earns $5 per week for doing chores. Jake wants to figure out how many weeks it will take for him to have at least enough money to buy a new tablet. Write an inequality and solve it to determine the number of weeks it will take.
Answer: 250 ≤ 100+5x
150≤5x divide by 5
30≤x
It will take 30 weeks to earn enough.
Step-by-step explanation:
Please Help! will Give Brainlest!
Answer:
tan ¤ = opp/adj
tan ¤ = 20/50
since opposite of the angle is 20, height of the tree is 20 feet.
Ans : D
Answer:
height : 20distance : 50Explanation:
[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
[tex]\hookrightarrow \sf tan(x)= \dfrac{20}{50}[/tex]
using the equation, we can identify that ↓opposite ( the height of the tree ) is 20adjacent ( the distance ) is 50pls help ! MAPPING SHAPES
A) only sequence a
b) only sequence b
c)both
d) neither
Given this regular pentagon and the side measurement of 6, find
the length of the apothem. round your answer to the nearest
hundredths.
The length of apothem for a regular pentagon and the sidemeasurement of 6 is 4.13 unit
What is apothem?
Apothemis a line segment from the center to the midpoint of one of the sides of a regular polygon .
The length of apothem (a) is given by:
[tex]a=\frac{s}{2*tan(\frac{180}{n} )} \\\\Where\ n\ is\ number\ of\ sides\ and\ s=side\ length\\\\Given:\\n=5,s=6, hence:\\\\a=\frac{6}{2*tan(\frac{180}{5} )}=4.13[/tex]
The length of apothem for a regular pentagon and the sidemeasurement of 6 is 4.13 unit
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is this correct if not whats the answer
Answer:
That answer is correct, when you do a survey, you pick people at random! So your answer is correct. :) If you have any more questions feel free to ask me. ^-^
Tanner made his father a quilt. The width is 6 5 /7 meters by 7 3/ 5 meters what is the area of the quilt?
Answer:
51.0285714…
Step-by-step explanation:
you just multiply them together.
Answer:
Step-by-step explanation:
→ Multiply the 2 lengths together
[tex]6\frac{5}{7} *7\frac{3}{5}[/tex]
→ Convert both to improper
[tex]\frac{47}{7} *\frac{38}{5}[/tex]
→ Multiply
[tex]\frac{1786}{35}[/tex]
→ Convert to mixed fraction
[tex]51\frac{1}{35}[/tex]
An angle measures 66° more than the measure of its supplementary angle. What is the measure of each angle?
A=
B=
Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?.
As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
Given function is:
[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]
What is a function?A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.
Divide the numerator and denominator of the given function by x.
[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]
[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]
As we know that as x approaches the infinity 1/x approaches 0.
So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]
[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]
Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
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write these polynomials in standard form
1). 5x^2- 15+7
2.) 4 + 8n- 3n^4＋ 10n2
Answer:
1. [tex]5x^{2} - 8[/tex]
2. [tex]NaN-16[/tex]
Step-by-step explanation:
which is the largest living thing?
Find a general formula for the nth term of the geometric series with
Answer:I think it would be the third one
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Which statement about a rotation is true? A. Rotating a right trapezoid around its vertical axis will form a cone. B. Rotating a square around its vertical axis will form a sphere. C. Rotating a right triangle around its vertical axis will form a cone. D. Rotating a rectangle around its vertical axis will form a sphere.
Rotating a shape involves moving it in a circular way around its axis
The true statement about the rotation is (c) Rotating a right triangle around its vertical axis will form a cone.
How to determine the rotation?When a two-dimensional shape such as triangles, trapezoid, square, rectangles, etc are rotated about their axes, the new shape formed is a three-dimensional shape
As a general rule, the rotation of a right triangle around its axis would form a cone.
Hence, the true statement about the rotation is (c)
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Answer: C. Rotating a right triangle around its vertical axis will form a cone.
Step-by-step explanation: CORRECT on Plato/Edmentum.
Find the value of x.
Answer:
38
Step-by-step explanation: subtraction:
Input interpretation: x: 105-67=
Ratio in lowest terms: 38
Division:
105/67= 1.56...=1 38/67---1R 38= 1 with the remainder of 38. So just 38.
The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.
By the above theorem, the equation is written as,
x + 67 = 107
Simplify the equation, then we have
x + 67 = 105
x = 105 - 67
x = 38°
The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.
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The box plots show the number of days spent at a national park by two different groups of visitors.
Two box plots are shown together. The title is Time Spent at Park. The number line goes from zero to five by a scale of one half. For Group A, the whiskers range from one half day to five days, and the box ranges from two days to three and one half days. A line divides the box at three days. For Group B, the whiskers range from one day to four and one half days, and the box ranges from two days to four days. A line divides the box at three and one half days.
Select all the statements that are supported by the random samples.
About 75% of visitors in Group A spent 3.5 days or more at a national park.
About , 75 %, of visitors in Group A spent , 3.5, days or more at a national park.
About 50% of visitors in Group B spent 3.5 days or less at a national park.
About , 50 %, of visitors in Group B spent , 3.5, days or less at a national park.
About 25% of both Groups A and B spent 2 days or less at a national park.
About , 25 %, of both Groups A and B spent , 2, days or less at a national park.
Group A had greater variability in the number of days spent at a national park.
Group A had greater variability in the number of days spent at a national park.
Group B had a greater median and a greater spread in the number of days spent at a national park.
The answer is B i took the quiz
Solve this linear system using determinants:
2x + 3y = 6
- 8x - 3y = 12
A=
Az =
[Ayl =
2×+3y=6
-8×-3y=12
-6×=18
×=18/-6
×=-3
——————
2×+3y=6
2(3)+3y=6
6+3y=6
3y=6-6
3y=0
Y=0/3
Y=0
——————
×=3
Y=0
————
2×+3y=6
2(3)+3(0)=6
6=6
xLasersx✨Please show the steps as well.
Answer:
x = 4Step-by-step explanation:
Rewrite the equation as
[tex]2^{x -1}=8\\[/tex][tex]2^{x -1}=2^3[/tex]Powers are equal if bases are same
[tex]x -1=3[/tex][tex]x=3+1[/tex][tex]x=4[/tex]~Hello! I will try to help you!
[tex] \Rightarrow \sf {2}^{x - 1} = 8[/tex]
»Convert the number 8 to a power of 2, then:-
[tex] \Rightarrow \sf {2}^{x - 1} = {2}^{3} [/tex]
»Because the bases on the right and left are the same, we will cross out the bases to produce a linear equation.
[tex] \Rightarrow \sf \cancel2 {}^{x - 1} = { \cancel2}^{3} [/tex]
»Let's find the value of x in the above equation!
[tex] \Rightarrow \sf x - 1 = 3 \\ \Rightarrow \sf x = 3 + 1 \\ \Rightarrow \bf x = 4[/tex]
With this it's done!
What is the area of H?
How many pieces of wood will be brought to complete the project?
Answer:
250
Step-by-step explanation:
Because if you multiply 10 by 10 you get 100 and then multiply 100by 2.5
Need Help! Given the drawing, what would the value of x need to be in order for it to be true that m || n ?
Answer:
13
Step-by-step explanation:
The theorem is that for a line bisecting two parallel lines, the oposite angles are equal. Hence, you can formulate the equation 4x+18 = 7x-21, which solves to 13.
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What polynomial has quotient x^2 + 6x − 2 when divided by x + 3?
Answer:
x³ + 9x² + 16x - 6
Step-by-step explanation:
First, you have to multiply x + 3 with x² + 6x - 2.
(x + 3)(x² + 6x - 2)
You will get:
x · x² = x³
x · 6x = 6x²
x · -2 = -2x
3 · x² = 3x²
3 · 6x = 18x
3 · -2 = -6
When you combine these, you get:
x³ + 6x² - 2x + 3x² + 18x - 6
Add them up to get your answer,
x³ + 9x² + 16x - 6.
Hope this helps!
what is the area of a triangle with a base with a length of 3 1/2 inches and a height of 3 inches
Answer: 5.25 square inches
Step-by-step explanation:
A=(1/2)bh=(1/2)(3.5)(3)=5.25