Answer:
BC = EF = 8
Step-by-step explanation:
Assuming you mean BC ≅ EF, then ...
... 3z +2 = z +6
... 2z = 4 . . . . . . . . add -2-z
... z = 2 . . . . . . . . . divide by 2
BC = EF = 2+6 = 8
The question is about finding the measures of given sides and angles in similar triangles. By setting up a proportion between the given sides BC and EF, we can solve for the variable 'z'. This 'z' can then be used to find the sides and angles of the triangles.
Explanation:In the case of the problem, we're dealing with the concept of similar triangles in geometry. Since △ABC is similar to △DEF, this means that the corresponding sides are in proportion, and corresponding angles are equal.
Given that BC = 3z + 2 and EF = z + 6, we can write a proportion: BC/EF = 3z+2 / z+6, because the lengths of the corresponding sides of these two similar triangles should be in ratio.
Then you can solve this equation for the variable 'z', which will give us the values for sides BC and EF. If necessary, you can also find the measure of the angles using the values of 'z'.
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PLEASE HELP ME ASAP: 99 points
for my career development class
you work for 40 hours a week at $8.75 an hour and pay 12% in taxes. What is your net pay?
Answer:
Net pay =$ 308
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - gross pay * tax rate
Simplifying this equation by factoring out gross pay
Net pay = gross pay (1- tax rate)
Gross pay = hours worked * hourly rate
Substituting this in
Net pay = hours worked * hourly rate (1- tax rate)
We know the
hours worked = 40
Hourly rate = 8.75
tax rate = .12
Net pay = 40 * 8.75 (1- .12)
Net pay = 350(.88)
Net pay =$ 308
HURRRRYYY 20 PTS
What is the midpoint of CD?
Answer: The correct option is
(A) [tex]\left(\dfrac{1}{2},-\dfrac{5}{2}\right).[/tex]
Step-by-step explanation: We are given to find the mid-point of the line segment CD shown in the graph.
From the graph, we note that
the co-ordinates of the endpoints of the line segment CD are (-3, -4) and D(4, -1).
We know that
the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) are given by
[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, he co-ordinates of the midpoint of line segment CD are
[tex]M=\left(\dfrac{-3+4}{2},\dfrac{-4+(-1)}{2}\right)=\left(\dfrac{1}{2},-\dfrac{5}{2}\right).[/tex]
Thus, the required midpoint of CD is [tex]\left(\dfrac{1}{2},-\dfrac{5}{2}\right).[/tex]
Option (A) is CORRECT.
The midpoint of the line segment between (-3, -4) and (4, -1) is (1/2, -5/2). Correct option is 1.
To find the midpoint of the line segment between two points (x1, y1) and (x2, y2), you can use the midpoint formula:
Midpoint (M) = ((x1 + x2) / 2, (y1 + y2) / 2)
Given the points (-3, -4) and (4, -1), let's find the midpoint:
Midpoint (M) = ((-3 + 4) / 2, (-4 + (-1)) / 2)
Midpoint (M) = (1 / 2, (-5) / 2)
Midpoint (M) = (1/2, -5/2)
So, the midpoint of the line segment between (-3, -4) and (4, -1) is (1/2, -5/2).
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Angle MNO is formed by segments MN and NO on the following coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A line segment MN is shown with M as ordered pair negative 1, 1 and N as ordered pair negative 5, 4. Another line segment NO is shown with O as ordered pair negative 1, 4.
Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. Which statement shows the measure of angle M′N′O′?
m∠ M′N′O′ = 90 degrees
m∠ M′N′O′ = 180 degrees
m∠ M′N′O′ = 2 ⋅ m∠MNO
m∠ M′N′O′ = m∠MNO
Answer:
I am 90% sure that the answer is M'N'O' is 90*
Step-by-step explanation:
A line segment MN is shown as M = -1,1 and N= -5,4 this makes a diagonal line across the grid. Another line segment NO is shown with O as ordered pair negative 1, 4. Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. this is where the angles meet, Rotating the shape (or the angles) does not change the degree of the angle of the shape. I am 99% sure that an 90* angle would be formed. but im just in middle school so what do i know?
Answer with explanation:
It is given that ,∠M NO is formed by segments MN and NO on the following coordinate grid.
Coordinate of Point M = (-1,1)
Coordinate of Point N= (-5,4)
Coordinate of Point O= (-1,4)
[tex]MN=\sqrt{(-1+5)^2+(1-4)^2}\\\\MN=\sqrt{16+9}\\\\MN=5\\\\NO=\sqrt{(-1+5)^2+(4-4)^2}\\\\NO=4\\\\MO=\sqrt{(-1+1)^2+(4-1)^2}\\\\MO=3[/tex]
MO²+NO²=MN²
So,By Pythagorean Theorem, ΔM NO is right Angled Triangle having ∠ O=90°.
Now, it is given that, ∠MNO is rotated 90 degrees counterclockwise about the origin to form ∠ M′N′O′.
⇒When we rotate a Triangle either Anticlockwise or Clockwise the triangle before Rotation and Triangle after rotation will be congruent to each other.
Option D:→
m∠ M′N′O′ = m∠M NO
Can someone please help me with problem 15 (picture)
$137,557.93
Step-by-step explanation:It is convenient to let a spreadsheet do the calculations. The number in the fourth column is the number in the first column divided by the number in the second column and multiplied by the number in the third column.
For example, the weighted average cost of Widgets is ...
... 135,320.00 × 866/2740 = 42,769.02
Then the total of all on-hand inventory is the sum of the inventory costs of the three items: $137,557.93.
the sales tax in your city is 4.4 and an item costs $3 before tax how much do u pay on the item
Answer:
$3.13
Step-by-step explanation:
We assume you mean the tax rate is 4.4%. Then the tax on $3 is ...
... tax = (tax rate) × (item cost)
... = 4.4/100 × 3.00 = 4.4 × .03 = 0.132 ≈ 0.13
The amount paid is ...
... amount paid = tax + item cost = $0.13 +3.00
... amount paid = $3.13
What is the effect on the graph of the function f(x)=x when f(x) is replaced with -1/2f(x)?
Answer:
The line will change its slope by a factor of -2 (line will now "point down" with twice the original steepness)
Step-by-step explanation:
f(x) = x | replace f(x) --> (-1/2)f(x)
(-1/2)f(x) = x
f(x) = -2x
Victor need 30 feet of rope. the rope he wants to buy is sold by the yard. he knows that there are 3 feet in 1 yard. how many yards should he But?
a. 10
b.20
c.60
d.90
Natalie chose D as the correct answer. how did she get that answer?
Douglas runs 4 1/4 miles each day.About how many miles does he run in seven days?Please show your work.
f(x) = -4x and g(x) = 5x-13, find f(g(x))
Answer:
-20x +52
Step-by-step explanation:
To solve this, we put the function g(x) into the function f(x) in the place of x
Put 5x-3 in for x in -4x
f(g(x)) = -4 (5x-13)
= -4*5x -4(-13)
= -20x +52
Find the correct values for the variables that make the statement cos(h)=x/y true.
H = °
x =
y =
Answer:
The sum of the measures of the angles in a triangle is equal to 180 degree.
In triangle FGH;
[tex]\angle F + \angle G + \angle H = 180^{\circ}[/tex]
or
[tex]\angle H = 180^{\circ} -{\angle F + \angle G}[/tex]
Substitute the given values from the given figure we have;
[tex]\angle H = 180^{\circ} -{33^{\circ} + 90^{\circ}}[/tex]
[tex]\angle H = 180^{\circ} -{123^{\circ}}[/tex]
Simplify:
[tex]\angle H = 57^{\circ}[/tex]
Given that:
[tex]\cos H = \frac{x}{y}[/tex]
Using Cosine ratio:
[tex]\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}[/tex]
In a given figure:
Base = GH = x and Hypotenuse = FH = y = 80 cm
Then;
[tex]\cos 57^{\circ}= \frac{x}{80}[/tex]
or
[tex]x = \cos 57^{\circ} \cdot 80[/tex]
[tex]x = 0.54463903501 \cdot 80 \approx 43.57[/tex] cm
Therefore, the value of :
[tex]H = 57^{\circ}[/tex]
x = 43.57 cm
y = 80 cm
The value of H is 57 degrees, x is 43.57, and y is 80 cm.
The sum of the measures of the angles in a triangle is equal to 180 degrees.
What is cosine function?The cosine is defined as the ratio of the base of the triangle and the hypotenuse of the triangle.
[tex]\rm Cosh= \dfrac{Base}{Hypotenuse}[/tex]
Where the value of base x is and Hypotenuse = FH = y = 80 cm.
The sum of the measures of the angles in a triangle is equal to 180 degrees.
Then,
In triangle FGH;
[tex]= \rm \angle F+\angle G + \angle H =180\\\\=90+33+\angle H =180\\\\\angle H = 180-90-33\\\\\angle H =180-123\\\\\angle H =57[/tex]
Substitute all the values in the formula;
[tex]\rm Cosh= \dfrac{Base}{Hypotenuse}\\\\Cos57=\dfrac{x}{80}\\\\x = Cos57 \times 80\\\\x=43.57 \ cm[/tex]
Hence, the value of H is 57 degrees, x is 43.57, and y is 80 cm.
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Which of the following statements is true?
All the answers are correct.
If a function has an inverse function, then the original function will pass the horizontal line test.
A function will always pass the vertical line test.
If the function has an inverse function, then the inverse function will pass the vertical line test.
Answer:
All the answers are correct
Step-by-step explanation:
Any relation that is a function will pass the vertical line test, regardless of any other characteristic it may have (such as being the inverse of some other function).
The inverse of a function is that function reflected across the line y=x. If the inverse passes the vertical line test (is a function), then the original must pass the horizontal line test. The reflection of a vertical line is a horizontal line and vice versa.
A textbook store sold a combined total of 266 math and biology textbooks in a week. The number of math textbooks sold was 54 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Let m and b represent the numbers of math and biology books sold, respectively. The problem statement tells you ...
... m + b = 266
... m - b = 54 . . . . . . . 54 more math books were sold
Adding these two equations gives you ...
... 2m = 320
... m = 160 . . . . . divide by 2
... b = 160 -54 = 106 . . . . 54 fewer biology books were sold.
160 math textbooks and 106 biology textbooks were sold in a week.
Chloe charged for admission to her play on three different nights. Each night, a different number of people were in attendance, but remarkably, Chloe collected $541 each night. If the admission charges for each child and each adult were $9 and $17, respectively, how many people in total came to the three showings?
To find the total number of people who came to the three showings, divide the total amount collected by the average admission price. Set up equations using the given information for each night and solve simultaneously to find the values of x, y, a, b, p, and q. Add those values to find the total number of people.
Explanation:To find the total number of people who came to the three showings, we need to divide the total amount collected by the average admission price. Let's calculate:
On the first night, let's assume there were x children and y adults. So, we can set up the equation.
9x + 17y = 541.
Similarly, for the second and third nights, we can set up two more equations:
9a + 17b = 541 and 9p + 17q = 541.
Solving these three equations simultaneously will give us the values of x, y, a, b, p, and q, which represent the number of children and adults present on each night. Adding those numbers together will give us the total number of people who came to the three showings.
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A)Simplify the expression and explain each step. 12 + 3(2y - 3) (B)Factor the expression completely. 18b - 12 (As you solve these problems do it with numbers intead of the word form like 1+1=2 instead of one plus one equals two, please and thank you. I will give brainlyist.
Answer:
A) 6y +3B) 6(3b -2)Step-by-step explanation:
A) Use the distributive property to eliminate parentheses. Then combine like terms. (The only "like terms" are the constants.)
... = 12 +3·2y +3·(-3) . . . use the distributive property to multiply each term in parentheses by the factor 3 outside those parentheses
... = 12 +6y -9 . . . . . . . . simplify
... = 6y + (12 -9) . . . . . . group like terms together
... = 6y + 3 . . . . . . . . . . simplify
___
B) Look for factors of each term that are also found in the other term.
... 18b has factors 3×6×b
... 12 has factors 2×6
The only common factor is 6, so we factor that out using the distributive property.
... 18b -12 = 6(3b -2)
_____
Comment on factoring
For factoring problems, it helps immensely if you know your times tables and some of the rules for divisibility. (Even numbers are divisible by 2, numbers ending in 0 or 5 are divisible by 5, numbers whose sum of digits is divisible by 3 are divisible by 3, for example.)
The three finalists in the talent show are Emily, Miguel, and Valerie. Their combined score is 24. Emily and Miguel's combined score is twice that of Valerie, and Valerie scored only one more point than Miguel. How many points did Emily score? Which equation is needed to represent the situation? A) e = m + 1 B) m = e + 1 C) m = v + 1 D) v = m + 1
Answer:
(i)
Emily's score was 9
(ii)
e = m + 2
Step-by-step explanation:
Let's assume
Emily's score is e
Miguel's score is m
Valerie's score is v
Their combined score is 24
so, we get
[tex]e+m+v=24[/tex]
Emily and Miguel's combined score is twice that of Valerie
we get
[tex]e+m=2v[/tex]
Valerie scored only one more point than Miguel
we get
[tex]v=m+1[/tex]
(i)
we got system of equations as
[tex]e+m+v=24[/tex].............(1)
[tex]e+m=2v[/tex]..................(2)
[tex]v=m+1[/tex]......................(3)
we can plug second equation into first one
[tex]2v+v=24[/tex]
[tex]3v=24[/tex]
[tex]v=8[/tex]
now, we can plug this into second and third equation
[tex]v=m+1[/tex]
we can plug it and find m
[tex]8=m+1[/tex]
[tex]m=7[/tex]
now, we can find e
[tex]e+7=2\times 8[/tex]
[tex]e=9[/tex]
So, Emily's score was 9
(ii)
we got
e=9
m=7
9=7+2
e=m+2
Answer: Emily's score is 9; Equation (D) v = m+1
Step-by-step explanation: To find Emily's score, let's represent each score with their own initials, i.e.: Emily's score is E; Miguel's score is M and Valerie's score is V.
Their combined score is 24, which means:
E + M + V = 24 (1)
Emily and Miguel's combined score is twice of Valerie, in other words:
E + M = 2V (2)
Valerie scored only one point more than Miguel:
V = M + 1 (3)
Substitute (3) into (2):
E + M = 2(M + 1)
E = 2M - M + 2
E = M + 2 (4)
With (3) and (4), use it to substitute into equation (1):
E + M + V = 24
M + 2 + M + M + 1 =24
3M = 21
M = 7
Using M=7 to find E:
E = M + 2
E = 7 + 2
E = 9
Emily's score is 9.
To represent the situation, the correct equation is V = M + 1, which means Valerie's score is 1 more than Miguel, which is exactly what's written in the question.
Mrs. Ryan plants 3 flowers along 4 in. of a garden row. The garden row is 3 ft long. How many flowers can she plant along the garden row? Enter your answer in the box.
Answer:27
Step-by-step explanation:
See Mrs. Ryan plants 3 flowers along 4 in. of a garden row.
The garden row is 3 ft long.
We know 1 ft = 12 inches
So, 3 ft = 36 inches
No. of flowers Length
3 4
x 36
So our equation becomes 4x = 36*3
equation, we get x = 36*3/4
= 27
Therefore, Mrs. Ryan can plant 27 flowers along the garden row.
Hope it helps!!!
WILL GIVE BRAINLIEST!! Which ratio is equivalent to the unit rate 30 miles 1 gallon ? How was the unit rate transformed into the equivalent ratio? A) 3 gallons 10 miles ; by dividing the numerator and denominator of the unit rate by 10. B) 90 miles 5 gallons ; by multiplying the numerator and denominator of the unit rate by 3. C) 6 gallons 180 miles ; by multiplying the numerator and denominator of the unit rate by 2. D) 180 miles 6 gallons ; by multiplying the numerator and denominator of the unit rate by 6.
Answer:
D)180 mi/6 gal; by multiplying the numerator and denominator of the unit rate by 6.
Step-by-step explanation:
30 mi/1 gal Multiply numerator and denominator by 6
= 180 mi/6 gal
A) and C) are wrong because they have gallons in the numerator
B) is wrong. It should be either 90 mi/3 gal or 150 mi/5 gal.
Lines l and k intersect forming two pairs of vertical angle. If one of these angles measure 120°, what are the measures of the other three angles?
The two lines intersect to form four angles. If one angle measures 120°, all the other three angles also measure 120° each.
Explanation:When lines l and k intersect, they form four angles. According to the properties of intersecting lines, opposite angles or vertical angles are equal. Therefore, if one angle is 120°, its vertical angle is also 120°. The sum of angles at a point is 360°, as the measurement around a point forms a complete circle. Hence, the other two angles, which are also vertical angles, will be 360° - (120°+120°) = 120° each. So, "all the angles in this case measure 120°".
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Using the number line, determine which expressions have a value that is greater than –8. Select Yes or No for each expression. l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l----l -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
Yes:
-13 +1
-6 -(-6)
-4 -(-7)
-4 - 6
-2 - 11
No:
yes
-6-(-6)-4-(-7)no
all othersStep-by-step explanation:Doing what the directions say is generally a good idea.
Adding a number moves to the right; subtracting a number moves to the left. Subtracting a negative number is the same as adding its opposite.
The arrowhead end of the line in the figure is the end result. Two of them end up to the right of -8, that is, greater than -8.
Answer:
Answer:
yes
-6-(-6)
-4-(-7)
no
all others
Step-by-step explanation:
the table shows the relationship between two variables which selection describes the relationship
Answer:
C. Decreasing; Linear.
Step-by-step explanation:
We have been given a table that shows the relationship between two variables.
Let us find slope of our given values using slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us find rate of change for points (1,5) and (2,-1)
[tex]m=\frac{-1-5}{2-1}[/tex]
[tex]m=\frac{-6}{1}=-6[/tex]
Let us find slope for points (3,-7) and (4,-13).
[tex]m=\frac{-13--7}{4-3}[/tex]
[tex]m=\frac{-13+7}{1}[/tex]
[tex]m=\frac{-6}{1}=-6[/tex]
We can see that rate of change is constant (-6), therefore, our function is a linear function. Since slope is negative (-6) and with each increase in x, our y is decreasing, therefore, our function is decreasing.
use natural logarithmics to solve the equation round to the nearest thousandth 3e^2x +5=26
x = 0.973
Step-by-step explanation:3e^(2x) +5 = 26
3e^(2x) = 21 . . . . . subtract 5
e^(2x) = 7 . . . . . . . divide by 3
2x = ln(7) . . . . . . . .take the natural log
x = ln(7)/2 ≈ 0.973 . . . . divide by 2 and evaluate
Answer:
x= .973
Step-by-step explanation:
3e^2x +5=26
Subtract 5 from each side
3e^2x +5-5=26-5
3e^2x =21
Divide by 3 on each side
3/3e^2x =21/3
e^2x =7
Take the natural log on both sides
ln (e^2x) =ln (7)
2x = ln (7)
Divide by 2
2x/2 = ln(7)/2
x = ln(7)/2
x is approximately .972955075
Rounding to the nearest thousandth
x = .973
Conrad has 6 more marbles than Rory. If r represents the numbers of marbles that Rory has, which expression represents the number of marbles that Conrad has?
Answer:
r+6
Step-by-step explanation:
r = marbles that Rory has
r+6 = marbles that Conrad has
Answer:
r+6
Step-by-step explanation:
r = marbles that Rory has
r+6 = marbles that Conrad has
you could also use c
The heights of two cylinders are in the ratio 3:1 if the volumes of two are same find the ratio of their respective radii
Answer:
[tex]\sqrt{3}[/tex] :1
Step-by-step explanation:
Ratio of height of two cylinders are 3:1
Let C2 has the height x
then height of C1 is 3x
Let r1 is the radius of C1
and r2 is the radius of C2
As given that volume of both are equal
Also we know that formula for the volume of the cylinder is
V= π r²h
for C1
V= π (r1)²h
for C2
V=π (r2)²h
As volume of both are same so equating them
π (r1)²h1 = π (r2)²h2
as h1 =3x and h2=x
putting values
π (r1)²(3x) = π (r2)²(x)
cancelling out π and x from both side of the equation
3(r1)²= (r2)²
Taking square root of both sides give
[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]
r1 ( [tex]\sqrt{3}[/tex]) = r2
or
r1 : r2 = [tex]\sqrt{3}[/tex] :1
I NEED THE ANSWER TO THIS QUESTION ASAP IF YOU ANSWER IT CORRECTLY I WILL LITERALLY WORSHIP YOU FOREVER:
Simplify the polynomials:
5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3
Note: The 5x^2zx isn't everything to the right is to the power; only 2 is raised to the power.
Answer:
12x^4y - 5x^5 - 2x^3z if im not mistake
Answer:
12x^4y -5x^5 -2x^3z
Step-by-step explanation:
The rule for exponents is (a^b)(a^c) = a^(b+c). Simply add the exponents of each of the variables in each term. Then examine the terms to see which are "like" terms (have the same constellation of variables). Combine those.
5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3
= 5x^(1+3)y +7x^(1+3)y -5x^(2+3) -5x(2+1)z +3x^3z
= 5x^4y +7x^4y -5x^5 -5x^3z +3x^3z
= (x^4y)(5+7) -5x^5 +(x^3z)(-5+3)
= 12x^4y -5x^5 -2x^3z
We often like to write these with the variable constellations in dictionary order and by decreasing degree, so ...
-5x^5 +12x^4y -2x^3z
A developer buys 12 acres of land at 41,00 per acre. How much does he pay for the land
Answer:
492,000
Step-by-step explanation:
Do 41,000x12. Pls mark me brainliest if im correct!
Which graph best represents the feasibility region for the system above
X>0
Y>x
Y<-1/4x+5
Answer:
See attached.
Step-by-step explanation:
The inequality x > 0 means the feasible region is to the right of the y-axis.
The inequality y > x means the feasible region is above the line y=x.
Only the first graph has these characteristics.
The feasibility region for the system of inequalities Y>X and Y<-1/4X+5 can be found by graphing both inequalities and finding the area that satisfies both at the same time. Y>X results in a line where the feasible region is above the line, while Y<-1/4X+5 produces a line where the feasible region is below it.
Explanation:The question is asking for the best graphical representation of the feasibility region for the system of inequalities Y>X and Y<-1/4X+5. Feasibility region in mathematics often refers to the set of all feasible solutions, which are the solutions that satisfy all constraints of the problem. In this context, it means finding the area of the graph that satisfies both inequalities at the same time.
One way to approach this is by graphing each of the inequalities on a two-dimensional plane. The inequality Y>X means that the Y-values are greater than the X-values. This will result in a graph where the feasible region is above the line Y=X.
On the other hand, Y<-1/4X+5 means that the Y-values are less than -1/4 times the X-values, plus 5. This produces a line with a negative slope, indicating that the feasible region is below this line.
The area that satisfies both these conditions represents the feasible region for the system of inequalities.
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3y <= -2x+18
-4y<=-x+12
which of the following points are in the solution set
select all that apply
A (-4,-3)
B (1,6)
C (2,4)
D (5,-5)
E (3,2)
Answer:
A (-4, -3)C (2, 4)E (3, 2)Step-by-step explanation:
It is convenient to use technology to plot the points and the functions to see what lies where. The first attachment shows such a plot.
_____
Of course, you can do the function evaluations. For example, testing answer B, we find ...
... 3·6 ≤ -2·1 +18 . . . . false for the first equation — not a solution
Checking all the points requires 10 function evaluations. When things get repetitive like that, I like to use a graphing calculator or spreadsheet.
_____
Using a calculator
The second attachment shows a calculator evaluating the viability of each point as a solution. The equations have been rearranged to ...
-2x -3y +18 ≥ 0-x +4y +12 ≥ 0This makes it easy to look at the evaluation results to see if the solution is viable or not.
The x-values of the points are entered into list L₁ and the y-values into L₂. The result of the first inequality above is in L₃ and the result for the second inequality is in L₄. Any negative value in L₃ or L₄ shows a point that is not part of the solution set. Points B and D fail to match problem requirements.
Points A, C, and E are in the solution set.
a candle burned at a steady rate. after 32 minutes, the candle was 11.2 inches tall. Eighteen minutes later, it was 10.75 inches tall. use an equation in point-slope form to determine the height of the candle after 2 hours.
ANSWER:
The candle was 12 inches tall to begin with.
After 2 hours (120 minutes), the height of the candle is approximately 9.9625 inches.
To start, let's define our variables:
t represents time in minutes.
h represents the height of the candle in inches.
First, we find the rate at which the candle is burning. The change in height over time is [tex]\( \frac{{11.2 - 10.75}}{{32}} \)[/tex] inches per minute.
Using point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and m is the slope, we can use the point [tex]\((32, 11.2)\)[/tex] and the calculated slope to find the equation of the line.
[tex]\( h - 11.2 = \frac{{11.2 - 10.75}}{{32}}(t - 32) \)[/tex]
Simplify to: [tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(t - 32) \)[/tex]
Next, we want to find the height after 2 hours (which is 120 minutes). Substituting t = 120 into the equation:
[tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(120 - 32) \)[/tex]
[tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(88) \)[/tex]
[tex]\( h - 11.2 = -1.2375 \)[/tex]
Now, solving for h :
[tex]\( h = 11.2 - 1.2375 \)[/tex]
[tex]\( h = 9.9625 \)[/tex]
So, after 2 hours (120 minutes), the height of the candle is approximately 9.9625 inches.
A carpet has a rectangular measure of 10 feet for the length and w feet for the width. If the perimeter is the sum of all four sides, then write an expression that represents the perimeter. Simplify.
2w – 20
2w – 10
2w +10
2w + 20
Answer:2w + 20
Step-by-step explanation:
See, the carpet has a rectangular measure of 10 feet.
It's width is 'w'
We, know that perimeter is the sum of all sides.
Now there are two equal sides which we consider length and two other equal sides for width.
So, we have to add all sides which gives 20 +2w
Also general formula for perimeter is 2(length + breadth)
So, our ans. is 2w + 20
Hope it helps!!!
Answer:
2w + 20
Explanation:
As stated in the question, the perimeter is the sum of the lengths of all the sides. So a general expression for the perimeter of a four-sided shape could be written like this:
P = AB + BC + CD + DA
or
P = 2w + 2l; w = width and l = length
So, to write an expression to match this problem, all we have to do is substitute the given side lengths (the first form) or substitute the given values of w and l (the second form):
P = AB + BC + CD + DA
P = 10 + w + 10 + w
P = 20 + 2w
P = 2w + 20
OR
P = 2w + 2l
P = 2(w) + 2(10)
P = 2w + 20
THIS IS A SUPER IMPORTANT TEST HELP!!!
Paul plans to spend p dollars for a meal at a restaurant and will leave a 20% tip. Paul writes the following expression to calculate the cost of the meal including the 20% tip:
p+0.20p
Which expressions are equivalent to the one Paul wrote?
Drag and drop each expression to the correct box to identify whether it is equivalent or not equivalent.
Equivalent Not Equivalent
2p+0.20 0.80p p(1+0.20) 1.20p 2.20p 1.02p
Answer:
1. Equivalent: [tex]p(1+0.20),\ 1.20p;[/tex]
2. Not equivalent: [tex]2p+0.20,\ 0.80p,\ 2.20p,\ 1.02p.[/tex]
Step-by-step explanation:
Consider the expression [tex]p+0.20p.[/tex]
Use the distributive property
[tex]a\cdot (b+c)=a\cdot b+a\cdot c.[/tex]
Then
[tex]p+0.20p=p\cdot 1+p\cdot 0.20=p\cdot (1+0.20)=p(1+0.20).[/tex]
Expression [tex]p(1+0.20)[/tex] is equivalent to the expression [tex]p+0.20p.[/tex]
Since [tex]1+0.20=1.20,[/tex] then expression [tex]p(1+0.20)=1.20p[/tex] is equivalent to the expression [tex]p+0.20p.[/tex]
All the rest expressions are not equivalent to the expression [tex]p+0.20p.[/tex]
Final answer:
The expressions equivalent to Paul's original expression p + 0.20p for calculating a meal's cost plus a 20% tip are p(1+0.20) and 1.20p. The other expressions provided do not accurately represent the original expression's intent to include a 20% tip.
Explanation:
The expression p + 0.20p can be simplified by combining like terms. As both terms contain 'p', we can add them together. Since 0.20 is the decimal form of 20%, this expression can be rewritten as 1p + 0.20p, which simplifies to 1.20p. This means that to find the total cost of the meal including the tip, you multiply the price of the meal 'p' by 1.20. Therefore, the equivalent expressions to p + 0.20p are p(1+0.20) and 1.20p, because both represent Paul adding a 20% tip to the cost of his meal.
Let's identify which of the given expressions are equivalent:
2p + 0.20 - Not equivalent, as it suggests doubling the price plus 20 cents.
0.80p - Not equivalent, as it represents only 80% of the original price.
p(1+0.20) - Equivalent; this is simply another way of writing the original expression.
1.20p - Equivalent; this is the simplified form of the original expression.
2.20p - Not equivalent, as it incorrectly represents an additional 220% of the meal cost.
1.02p - Not equivalent, as it only adds an additional 2% to the original price, not the 20% intended for the tip.