How tall is a pole if a 40 ft guy wire reaches from the top of that pole
to a point on the ground 19 ft from the bottom of the pole?
Lamar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $10, and paint and canvas for each painting costs $45; he will sell each painting for $50. Once Lamar sells a certain number of his paintings, he will be breaking even. How many paintings will that be?
Answer:
2
Step-by-step explanation:
If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.
50x = 45x + 105x = 10x = 2The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.
What is breakeven?In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."
Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.
Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,
Total cost of x painting = $10 + $45(x)
Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,
Revenue generated = $50(x)
Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,
Total cost of x painting = Revenue generated
$10 + $45(x) = $50(x)
10 + 45x = 50x
10 = 50x - 45x
10 = 5x
x = 10/5
x = 2
Hence, For breakeven Lamar needs to sell 2 paintings.
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Write an equation of the line that passes through (3,-2) and is parallel to the line y = 2x + 4.
Answer: [tex]y+2=2(x-3)[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so substituting into point-slope form, the equation is
[tex]y+2=2(x-3)[/tex]
According to indical equation solve 3×=1\81
Answer:
x = - 4
Step-by-step explanation:
using the rule of indices
[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then
[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is
[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus
x = - 4
Tell if each pairs of segments are congruent
Yes/No
A. AB and BC
B. AC and BD
A. No, AB and BC are not congruent
B. No, AC and BD are not congruent
Calculating length of a segmentFrom the question, we are to determine if the given pairs of segments are congruent
To do this, we will determine the length of the line segments
Consider the given number line,
AB = -2 - (-5) = -2 + 5 = 3
BC = 0 - (-2) = 0 + 2 = 2
AC = 0 - (-5) = 0 + 5 = 5
BD = 5 - (-2) = 5 + 2 = 7
Now,
A. AB and BC
AB = 3 and BC =2
∴ AB and BC are not congruent.
Thus, No
A. AC and BD
AC = 5 and BD = 7
∴ AC and BD are not congruent.
Thus, No
Hence,
A. No, AB and BC are not congruent
B. No, AC and BD are not congruent
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Which of the following proves these triangles are congruent
Answer:
SAA
Step-by-step explanation:
Identify the corresponding congruent parts as either sides or angles. Look at their order of appearance around the triangle.
Corresponding partsThe sides marked with a single hash mark are identified as corresponding and congruent.
The angles marked with a single arc are identified as corresponding and congruent.
The vertical angles where the lines cross are congruent.
SequenceWorking counterclockwise around the left triangle, we encounter ...
side marked congruentvertical angles (congruent)angle marked congruentThese same features appear in the same order working counterclockwise around the triangle on the right.
The "side," "angle," and "angle" are referenced in the congruence postulate as S, A, and A.
Congruence is proved by the SAA congruence postulate.
Given the linear function of 3x-7y=14, determine the ordered pair where the line crosses the y axis. Remember to write your answer in form (x,y)
Answer:
(0, -2)
Step-by-step explanation:
The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.
3x - 7y = 14
3*0 - 7y = 14
-7y = 14
y = -2
Becca polled the members of her volleyball team to see what their opinions were regarding the awards banquet. Her results were:
A total of 16 people wanted the steakhouse option.
• Seafood buffet but not bsteakhouse: 8
Steakhouse but not seafood buffet: 9
.neither 4
Based on the total number of people who want the steakhouse option, the probability that a student will not want the seafoodbuffet if they want the steakhouse option is 24%
What is the probability of the students' choice?The probability that a student does not want the seafood buffet given that they want the steakhouse option is:
= Number of people who want steakhouse but not seafood / Total surveyed
Solving gives:
= 9 / (16 + 8 + 9 + 4)
= 9 / 37
= 24%
Full question is:
If a student wants the steakhouse option, what is the probability that they will not want the seafoodbuffet?
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f(x)=4x+1 and g(x)=2x2+1, find (f∘g)(x) and (g∘f)(x)
The value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Composite functionsComposite function is also known as function of a function. They are determined by representing x with the other function.
Given the following functions
f(x)=4x+1
g(x)=2x^2+1
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(2x^2+1)
(f∘g)(x) = 4(2x^2+1) + 1
(f∘g)(x) =8x^2 + 5
For the composite function (g∘f)(x)
(g∘f)(x) = g(f(x))
(g∘f)(x) = g(4x+1)
Replace x wit 4x+1 to have:
(g∘f)(x) = 2(4x+1)^2 + 1
(g∘f)(x)= 2(16x^2+8x+1) + 1
(g∘f)(x) = 32x^2 + 16x + 3
Hence the value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
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ill give brainliest
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
The aim of factorization to obtain the common factors that are present in the expression.
What are factors?When we factorize an expression, the aim is to obtain the common factors that are present in the expression.
Now we have trinomials numbered 1 - 15. Trinomial is an expression that is made up of three terms. Quadratic expressions are mostly found to appear as trinomial
The binomial factors that are associated with each are shown in the factorized expressions below. The binomials contain two terms in each bracket.
Given the trinomials, the correct binomial factors are;
(x−1)(x+7) (x−2)(x−3)(x+1)(x−7) (x−1)(x+6)(x−3)(x+4)(x+2)(x−4)(x+1)(x−5)(x−1)(x+3) (x+4)(x−4)(x+3)(x−4)(x−3)(x−6)(x+2)(x−7)(x−2)(x−5) (x−3)(x−8) (x+5)(x−6)Learn more about factorization:https://brainly.com/question/19386208
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Image is attached below, please help. Thank you so much!
The limit of f(x) as x goes to 1 will not exist for function III.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. For a function with different lateral limits at a point x = a, the limit will not exist at the point x = a. Additionally, the limit may not exist at a point if there is a non-removeable discontinuity.
Factoring the function 1, the limit will be given as follows:
[tex]\lim_{x \rightarrow 1} \frac{1 - x^2}{x - 1} = \lim_{x \rightarrow 1} \frac{(1 - x)(1 + x)}{x - 1} = \lim_{x \rightarrow 1} -(1 +x) = -2[/tex]
Hence the limit exists.
Factoring the function 2, the limit will be given as follows:
[tex]\lim_{x \rightarrow 1} \frac{x^2 - x^3}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x^2(1 - x)}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} -\frac{x^2}{x + 1} = -\frac{1}{2}[/tex]
Hence the limit exists.
Factoring the function 3, the limit will be given as follows:
[tex]\lim_{x \rightarrow 1} \frac{x + 1}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x + 1}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} \frac{1}{x - 1}[/tex]
Non-revemoveable discontinuity, as we can't remove x - 1 for the denominator, ence the limit does not exist for function III.
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PLEASE HELP ME !” ASAP?
Answer:
39°
Step-by-step explanation:
Opposite angles of a parallelogram are congruent.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
" The opposite angles of a Parallelogram are always equal to one another "
[tex] \qquad \large \sf {Conclusion} : [/tex][tex] \qquad \large \sf {Conclusion} : [/tex]
Angle M = Angle N = 39°Find the product. Write your answer in exponential form. 8^-2•8^-9
Answer:
8 ^-11
Step-by-step explanation:
It should be noted that in this case, since it's the product that we want to get, it's important to add the power together. This will be:
8^-2 × 8^-9
= 8^(-2 + -9)
= 8^-11
2. The product of two consecutive even numbers is 168. What are the numbers?
Answer:
12 and 14
Step-by-step explanation:
12 * 14 = 168
Answer:
12 & 14
Step-by-step explanation:
the work: x = first even number, (x+2) = second even number
The equation
[tex]x(x+2)=168[/tex]
[tex]x^{2} +2x=168[/tex]
[tex]x^{2} +2x-168=0[/tex]
Factoring
[tex](x-12)(x+14)=0[/tex]
first factor
[tex]x-12=0\\x=12[/tex]
Second factor
[tex]x+14=0\\x=-14[/tex]
The solution is the positive number
x = 12 is the first even number
x + 2 = 12 + 2 = 14 is the second even number
Hope this helps
1 gallon of paint covers 300 ft how many gallons I needed for a room 30 ft long 20 ft wide by 12 ft high
Answer:
6 gallons
Step-by-step explanation:
the total area to be painted :
= The total surface area - area of the floor
= area of the walls + area of the ceiling
area of the walls :
= [perimeter of the room] ×height
= [2 × (30+20)] × 12
= 1 200
area of the ceiling :
= length × width
= 30 × 20
= 600
the total area to be painted :
= 1200 + 600
= 1800
The number of gallon of paint needed to cover the room :
= 1800 ÷ 300
= 6
– 30% OF THE CELL PHONE USERS TODAY USE A MOTOROLA
PHONE. DETERMINE THE PROBABILITY THAT IF SIX CELL PHONE USERS
ARE SELECTED AT RANDOM, EXACTLY FOUR OF THEM USE A MOTOROLA CELL
PHONE.
Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
p = 0.3, n = 6.
The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595
0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
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Which equation can be simplified to find the inverse of y = 5x^2 + 10?
Answer:
Step-by-step explanation:
Here's the solution
f^(-1)(x)=(\sqrt(5(x-10)))/(5), -(\sqrt(5(x-10)))/(5)
PLWASW HELP ALOT OF POINTS Charlie used construction paper, scissors and a ruler to construct an
isosceles triangle with a pair of sides each 3 inches long and an acute
angle on top. He drew an altitude from the acute angle to the base and
wrote down his observations. He then created another isosceles triangle
with a pair of sides of 7 inches long with an obtuse angle on top, drew a
altitude to the base, and recorded his observations.
Which of these is the best conjecture for Charlie to develop?
The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
What is conjecture?It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.
From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.
Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
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Question: 2 Based on the mass of lactose of 0.28 grams in 1 mL of skim milk, calculate the percent composition of lactose in skim milk.
Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.
Mass volume percentThe concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.
Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.
In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:
[tex]Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100[/tex]
This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.
Percent composition of lactose in skim milkIn this case, you know:
mass solute= 0.28 gramsvolume solution= 1 mLReplacing in the definition of mass volume percent:
[tex]Mass volume percent=\frac{0.28 grams}{1 mL}x100[/tex]
Solving:
mass volume percent= 28 %
Finally, the percent composition of lactose in skim milk is 28%.
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6) Evaluate 4x if x = -1/4
Answer: -1
Step-by-step explanation:
Evaluate 4x if x = -1/4
4(-1/4) = -1
Answer: -1
Step-by-step explanation:
4x and x = -1/4
plug x into the expression
[tex]4(-\frac{1}{4} )[/tex]
simplifies to:
[tex]-\frac{4}{4}[/tex]
4 divided by 4 is just 1, but it is negative so your final answer is
-1
Hello please help asap!! i will mark brainliest and this is worth 20 points!!!!! tysm
The least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors. This can be obtained by simply giving colors to the small shapes according to the criteria.
What is the least number of colors?From the question the figure, the number of colored sections with which are not colored with respect to a "touching" colored section, would not be half of the total colored sections since the sections are not alternating as they still meet at a common point.
After all, it notes no two touching sections, not adjacent sections.
There is no equation to calculate this requirement with respect to the total number of sections.
Taking one triangle or square as the starting we can give colors to each small units. This figure will be the start of sequence of other small figures.
If a square were to be this starting shape that have same color as that color of the square.
Now from the remaining given another color to the starting figure. We will get that shapes, that will have same color.
Like that the remaining figures are given colors.
Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.
Hence the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors.
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14. A photograph measures eight inches wide and ten inches long. The picture is enlarged to fit on a wall. If the new larger picture is 208 inches wide, how long is it?
Answer:
The file contains the solution to the question
if two vertical angles are 2x-10 and x+20 find the value of x
Answer:
x=70
Step-by-step explanation:
when added together, verticle angles equal 180 degrees.
2x-10+x+20=180
3x-10+20=180
3x-30=180
3x=210
x=70
HELP ASAP WILL GIVE BRAINLIEDT IF CORRECT!!!!!!!
Find the equation to the line below
Answer:
y = 3/2x + 2
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = 3/2x + 2
Answer:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
Step-by-step explanation:
Equation of line:Pick any two points on the line.
(0,2) and (2 , 5)
(0,2) ⇒ x₁ = 0 & y₁ = 2
(2,5) ; x₂ = 5 & y₂ = 5
[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{5-2}{2-0}\\\\=\dfrac{3}{2}[/tex]
Equation of line in point slope form:
[tex]\sf y - y_1 =m(x -x_1)[/tex]
Point(0 ,2) and m = 3/2
[tex]\sf y - 2 = \dfrac{3}{2}(x -0)\\\\ y - 2 = \dfrac{3}{2}x\\\\[/tex]
Equation of line in slope y-intercept form:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
After 3 minutes, a submarine had descended to −550 feet. After 8 minutes, the submarine had descended to −600 feet. Assuming a linear function, write an equation in the form d(t)=mt+b that shows the depth, d(t), after t minutes.
Answer:
d(t)=-10t-520
Step-by-step explanation:
First you have to find the gradient (m) using the formula [tex]m=\frac{d(t)2-d(t)1}{t2-t1}[/tex]
using the two points you have been given: 1(3,-550) and 2(8,-600)
so you substitute these points into the equation [tex]m=\frac{-600+500}{8-3}[/tex]
m=-10
Now that you have found the m-value you need to find the b-value by using one of the points you already have, I will use Point 2 (8,-600), and substitute it into the equation and solve
d(t)=-10t+b
-600=-10*8+b
-600=-80+b
-520=b
Therefore, the equation is d(t)=-10t-520
If A= {1,2,3,4,5},B= {1,3,5,7}and C= {2,4,6,8}
Step-by-step explanation:
Intersection of A and B={1,3,5}Intersection of B and C={ }B - A={1,3,5,7} - {1,2,3,4,5} ={1,7}Given that 3 is a root of a given polynomial, what can you say is a factor of that polynomial?
The factor of such equation described as having the number 3 as a root can be determined as; (x-3).
What is a possible factor of a given polynomial whose root is 3?It follows from the task content that; we are required to determine a possible factor of a polynomial in the event that such polynomial has a root of 3.
The implication of a polynomial having a root of 3 is that; such a polynomial has 3 to be one of it's zeros.
Hence, a linear equation which holds for such polynomial is that; x = 3 and when expressed as a linear factor, the linear factor is; (x-3).
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Interpreting Slope in a Line of Best Fit
Use the scatterplot and equation to answer the question.
AY
180+
160+
140+
120+
100+
80+
Number of Customers Served
2
60+
40+ y= 17.9x+6.67
20+
3 4 5 6 7 8 9
Number of Hours
x
The data reflects the number of hours an employee
spends working a checkout line (x), paired with the
number of customers served (y). How can the slope of
the line be interpreted?
With each additional hour, between 6 and 7
customers are served.
With each additional hour, nearly 18 customers are
served.
Each additional customer requires 17.9 minutes to
check out.
O Each additional customer requires 6.67 minutes to
check out.
Done
Answer:
b
Step-by-step explanation:
b
solve the algebraic equation 7 x - 2 equals to 2x + 13
Answer:
x = − 6
Step-by-step explanation:
I have my work
What is 6 wholes divided by 2/3 ?
Answer:
9
Step-by-step explanation:
6 ÷ 2/3 = 6 / (2/3 ) = (6/1) / (2/3) = 6/1 x 3/2 = 18/2 = 9