The formula to convert degrees Fahrenheit to Celsius is:
[tex]\bf{^{\circ}C=\dfrac{5}{9}(^{\circ}F-32) \ \ \to \ \ \ Formula }[/tex]
Convert 59°F to degrees Celsius.
Add the number 59 in the formula, and solve.
[tex]\bf{=\dfrac{5}{9}(59-32) }[/tex]
Subtract 32 from 59.
[tex]\bf{=\dfrac{5}{9}(27) }[/tex]
Multiply 5 x 9 = 135, then divide 135/9 = 15.
[tex]\bf{=15 \ ^{\circ}C}[/tex]
Therefore 59 °F = 15 °C. The correct option is "D".
{ Pisces04 }If f(x) is a linear function, what is the value of n?
X
-4
-1
n
2
O 4
05
09
f(x)
-25
-10
20
Answer:
3rd option : 5
Step-by-step explanation:
https://brainly.com/question/8346797
its a slope question
f(x) is y
y2-y1/x2-x1
-10+25/-1+4
15/3
5
Since we know that the equation of a line in slope-intercept form is: , where, m= Slope and b= y-intercept.
Upon substituting m = 5 in slope-intercept form of equation we will get,
Now let us find y-intercept by substituting coordinates of one point in our given line.
So the equation of given line will be,
Now let us find value of n by substituting x = n and y = 20 in our equation.
Therefore, the value of n is 5.
A counter in Lamar's kitchen is 1 yard wide and 2 yards long. Lamar wants to replace the counter with a granite countertop, which would cost $204.63 per square yard. How much would the granite countertop cost?
Answer:
Step-by-step explanation:
Comment
Find the number of square yards
Area = L * w
L = 2
w = 1
Area = 2 * 1
Area = 2
Now for the counter top
1 sq yard costs 204.63
2 sq yards cost 2 * 204.63
2 sq yards cost 409.26
Answer: 409.26
The total surface area of a closed cylinder is
5000 cm2
find the dimensions of the cylinder that
maximize its volume and state this maximum
volume.
verify that it is a maximum point.
The maximum volume of the cylinder is 27147.355 at the maximum point [tex]r = \frac{50}{\sqrt{3} }[/tex] .
How do you find the maximum volume of the cylinder?The formula for the volume of the cylinder v = [tex]\pi[/tex][tex]r^{2}[/tex]h, To find the maximum volume of the cylinder we apply the condition of maxima [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0.
Let r cm be the radius and h cm be the height of the closed cylinder.
Then, Total surface area of the cylinder = [tex]2\pi r(r+h)[/tex]
[tex]5000[/tex] = [tex]2\pi r^{2} +2\pi rh[/tex]
[tex]h[/tex] = [tex]\frac{5000-2\pi r^{2} }{2\pi rh}[/tex] .............(1)
Volume of the cylinder v = [tex]\pi r^{2} h[/tex]
Substitute the value of [tex]h[/tex] in the above equation
[tex]\Rightarrow[/tex] = [tex]\pi r^{2}[/tex] × [tex]\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ][/tex]
[tex]\Rightarrow[/tex] = [tex]\frac{r}{2}[/tex] × [tex](5000-2\pi r^{2} )[/tex]
[tex]\Rightarrow[/tex] v = [tex]2500r-\pi r^{3}[/tex] ..............(2)
Now, for the maximum volume of the cylinder [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0
[tex]\Rightarrow[/tex] [tex]\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0[/tex]
[tex]\Rightarrow[/tex] [tex]3\pi r^{2} = 2500[/tex]
[tex]\Rightarrow[/tex] [tex]r^{2} = \frac{2500}{3\pi }[/tex]
[tex]\Rightarrow[/tex] [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]
Volume is maximum for [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]
Then, v = [tex]2500r-\pi r^{3}[/tex]
[tex]\Rightarrow[/tex] = [tex]2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}[/tex]
[tex]\Rightarrow[/tex] = [tex]\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }[/tex]
[tex]\Rightarrow[/tex] = [tex]\frac{125000}{\sqrt{3\pi } }[/tex]×[tex]\frac{2}{3}[/tex]
[tex]\Rightarrow[/tex] = [tex]\frac{250000}{3\sqrt{3\pi } }[/tex]
[tex]\Rightarrow[/tex] v = 27147.355
Hence, The maximum volume of the cylinder is 27147.355 at the maximum point [tex]r = \frac{50}{\sqrt{3} }[/tex] .
To learn more about total surface area and volume of the cylinder from the given link
https://brainly.com/question/16095729
#SPJ4
A right triangle has side lengths AC = 7 inches, BC = 24
inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
A) mZA= 46.2°, mZB=43.8°, mZC=90°
B) mZA= 73.0°, mZB= 17.0°, mZC = 90°
C) mZA 73.7°, mZB= 16.3°, mZC = 90°
D) mZA 74.4°, mZB= 15.6°, mZC = 90°
Therefore, the measures of the angles in triangle ABC is as follows:
m∠A 73.7°, m∠B = 16.3°, m∠C = 90°How to find angles of right triangle?The measure of the angles in the right triangle can be found as follows:
Using trigonometric ratios,
sin ∅ = opposite / hypotenuse
sin ∅ = 7 / 25
∅ = sin ⁻¹ 0.28
∅ = 16.2602047083
∅ = 16.3°
Hence,
m∠B = 16.3°
m∠C = 90°
m∠A = 180 - 90 - 16.3 = 73.7°
learn more on right triangle here: https://brainly.com/question/27899600
#SPJ1
AVERE
Given: P(0, -13) and 7(15,-7)
What is the slope of PT?
Answer:
2/5
Step-by-step explanation:
To find the slope of a line segment, find the difference in y and divide by the difference in x (delta y / delta x)
Delta y: -7 - (-13) = 6
Delta x: 15 - 0 = 15
Slope = delta y / delta x
Slope = 6/15 = 2/5
If this helped, I really would appreciate if you tagged as brainliest!
HELP FAST! What is the equation of the line graphed?
(y=mx+b)
What is the pattern in the values as the exponents increase?
Powers of 2
Value
2 Superscript negative 5
StartFraction 1 Over 32 EndFraction
2 Superscript negative 4
StartFraction 1 Over 16 EndFraction
2 Superscript negative 3
StartFraction 1 Over 8 EndFraction
2 Superscript negative 2
One-fourth
2 Superscript negative 1
One-half
2 Superscript 0
1
add StartFraction 1 Over 16 EndFraction to the previous value
subtract StartFraction 1 Over 16 EndFraction from the previous value
divide the previous value by 2
multiply the previous value by 2
The pattern in the values as the exponents increase is multiply the previous value by 2.
What is exponents and powers?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
Given:
Powers of 2 Values
[tex]2^{-5}[/tex] 1/32
[tex]2^{-4}[/tex] 1/16
[tex]2^{-3}[/tex] 1/8
[tex]2^{-2}[/tex] 1/4
[tex]2^{-1}[/tex] 1/2
As, from the given data we can see that negative powers of 2 reducing by 1.
as, 2^-5 * 2= 2^-4
Hence, multiply the previous value by 2 to obtain the next value.
Learn more about exponents and powers here:
https://brainly.com/question/16649216
#SPJ1
millimeters =equals 15centimeters 4millimeters
This shows that 154mm is equivalent to 15centimeters 4millimeters
Conversion of unitsUnits are measure of a quantity. From the given question, we are to convert 15cm4mm to millimeters
Since 10mm =1cm, hence;
15cm4mm = (15 * 10) + 4
15cm4mm = 150+ 4
15cm4mm = 154mm
This shows that 154mm is equivalent to1 5centimeters 4millimeters
Learn more on unit conversion here: https://brainly.com/question/3371568
#SPJ1
Area= in2
Help me please!! Thank you so much
Answer:
60 in²
Step-by-step explanation:
Area of a Regular Polygon
[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]
where:
A = arean = number of sidess = length of one sidea = apothem (the line drawn from the center of any polygon to the midpoint of one of the sides)From inspection of the diagram:
n = 5s = 6 ina = 4 inSubstitute the values into the formula and solve for A:
[tex]\implies \sf A = \dfrac{5 \times 6 \times 4}{2}[/tex]
[tex]\implies \sf A = \dfrac{120}{2}[/tex]
[tex]\implies \sf A = 60\:in^2[/tex]
Therefore, the area of the given regular pentagon IJKLM is 60 in².
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{First thing, let's get the formula for}\\\huge\textbf{the regular pentagon/polygon.}[/tex]
[tex]\mathbf{\dfrac{1}{2}\times \boxed{a}pothem\times\boxed{p}erimeter = {\boxed{a}rea}}[/tex]
[tex]\huge\textbf{Or we could simply say....}[/tex]
[tex]\mathbf{\dfrac{\boxed{n}umber\ of\ sides\ you\ have \times \boxed{s}ide \ length\ on\ one\ side\times \boxed{a}pothem}{2} = \boxed{a}rea}[/tex]
[tex]\huge\textbf{Let's plug the pieces to the equation,}\\\huge\textbf{since we have that information out the}\\\huge\textbf{way.}[/tex]
[tex]\bullet\mathbf{\ Number\ of\ sides \rightarrow \boxed{\bf 5}}[/tex]
[tex]\bullet\mathbf{\ Side\ length\ of\ one\ side \rightarrow \boxed{\bf 6\ inches}}[/tex]
[tex]\bullet\mathbf{\ Apothem \rightarrow \boxed{\bf 4\ inches}}[/tex]
[tex]\huge\textbf{Making the equation for you:}[/tex]
[tex]\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}[/tex]
[tex]\huge\textbf{Solving for the result:}[/tex]
[tex]\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}[/tex]
[tex]\mathbf{\dfrac{30\times 4}{2} = \boxed{a}rea}[/tex]
[tex]\mathbf{\dfrac{120}{2} =\boxed{a}rea}[/tex]
[tex]\mathbf{\dfrac{120\div2}{2\div2} = \boxed{a}rea}[/tex]
[tex]\mathbf{\dfrac{60}{1} = \boxed{a}rea}[/tex]
[tex]\mathbf{60\div1 = \boxed{a}rea}[/tex]
[tex]\mathbf{60 = \boxed{a}rea}[/tex]
[tex]\huge\textbf{Met the result....}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{60\ in^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assingment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A painting measures b meters by 4 meters. a frame shop charges $10 per meter for a wooden frame. how much would it cost to buy a frame for the panting?
$ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame. This can be obtained by finding the perimeter of the painting and multiplying with the cost of wood per meter.
What is the cost of buying a frame for the painting?
Given that,
length of the painting (l) = b meters
width of the painting (b) = 4 meters
Perimeter of the painting = 2(l+b)
= 2(b+4)
= 2b + 8
Cost of the frame = (2b + 8)× $10 per meter
= $ (20b + 80)
Hence $ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame.
Learn more about finding cost of frame:
brainly.com/question/16757070
#SPJ4
Jesse had $80 in his checking account. A month
later, his checking account balance was -30. Which
expression represents the difference between the
two checking account balances?
Answer:
80 - 30
Step-by-step explanation:
I'm just guessing
The table below shows the x variable for a table. Choose a corresponding y table that will create a direct variation.
Answer:
table A
Step-by-step explanation:
A direct variation can be expressed as: [tex]\frac{y}{x}=k[/tex]. The y/x is equal to a constant value k. Multiply both sides by x you get: [tex]y=kx[/tex]. So as x increases by 1, y increases by some constant value. So to find which one will create a direct variation, see which of the tables has a constant y/x
Table A:
7/2 = 3.5
14/4 =3.5
17.5/5=3.5
21/6 = 3.5
this has a constant y/x so it is a direct variation
Table B:
7/2 = 3.5
14/4 = 3.5
21 / 5 = 4.2
this is not a direct variation, it doesn't have a constant y/x
table C:
7 / 2 = 3.5
14 / 4 = 3.5
15/5 = 3
This is not a direct variation, it doesn't have a constant y/x
table d:
7/2 = 3.5
14/4 =3.5
17/5=3.4
This is not a direction variation, it doesn't have a constant y/x
Select the correct answer.
Which equation is equivalent to the formula below?
y = a (x − h)² + k
PADED
HODIN BARISTLE
DEKKING
y k
-
OA G = (1²=51²
(I h)²
-
OB.
h = x = ( ² = ²)²
a
O C.
* = ± √/² = ²
X
OD. k = y + (x - h)²
- h
-
Answer:
a.
Step-by-step explanation:
a= y-k/ (x-h)^2
Make me a brain listUse the Venn diagram shown.
A Venn diagram with overlapping circles A and B. Circle A includes the elements 1, 3, 7, 8, and 11. Circle B includes elements 2, 3, 6, 7, and 12. The area outside the circles is labeled Q, which contains elements 9 and 17.
What are the elements of (A ∩ B)?
{1, 2, 3, 6, 7, 8, 11, 12}
{1, 2, 6, 8, 11, 12}
{9, 17}
{3, 7}
Since intersection means the element in set A that are also in set B, hence (A ∩ B) = {3, 7}
Unions and Intersection of SetsSets are arrangements of elements in a specific order. Given the following sets.
A = {1, 3, 7, 8, 11}
B = {2, 3, 6, 7, 12}
Determine the intersection of A and B
Since intersection means the element in set A that are also in set B, hence;
(A ∩ B) = {3, 7}
Hence the elements of (A ∩ B) is {3, 7}
Learn more on intersection of sets here: https://brainly.com/question/11439924
#SPJ1
Answer:
D) (3,7)
Step-by-step explanation:
P(AnB) mean intersection, which is (3,7)
P(AUB) mean Union
However. if the question was asking this "What are the elements of P(AUB) then the answer would be A) {1, 2, 3, 6, 7, 8, 11, 12}.
But the question was asking for P(AnB) which is D) (3,7)
Select
Select the correct answer from each drop-down menu.
Which system of Inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
The inequality equation of the lines are given as 4x – y ≤ 4 and 2x – 2y ≤ 3. Then the correct option is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The graph is given below.
From the graph, equation of the lines are given as
4x - y = 4 and 2x - 2y = 3
But for the inequality is shown in graph. Then the inequality equation of the lines are given as
4x – y ≤ 4 and 2x – 2y ≤ 3
Then the correct option is A.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ1
Tan0=
A)1/cos
B) 1+sec^2 0
C) 1- cot^2 0
Find the sum of the first ten prime numbers. Find the sum of the first ten prime numbers .
The sum of the first ten prime numbers is 129.
What is a prime number?The prime numbers are those numbers that have only one factor namely 1 and the number itself.
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Their sum is
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29
= 129
Hence, the sum of the first ten prime numbers is 129.
Learn more about prime numbers;
https://brainly.com/question/4184435
#SPJ1
The students at Midtown Middle school sold flowers as a fundraiser in September and
October. In
October, they charged $1.50 for each flower. The October price was a 20%
increase of the September price.
Part A
What was the price of the flowers
in September?
Enter your answer in the box.
L.25
Part B
The seventh-grade class earned 40% of the selling price of each flower.
In September, they sold 900 flowers.
In October, they sold 700 flowers.
Select a choice from each drop-down menu to make a true statement.
The seventh-grade class earned more money in September
by Choose one.
Help with part b pls
The price of flowers in September exists $1.25.
Total money released in October = $420.
The class gained more money in September and they gained $30 better than in October.
How to estimate the price of the flowers in September or October?Part A
Let the cost of flowers in September be x, then
(100 + 20)/100 [tex]*[/tex] x = $1.50
120/100 [tex]*[/tex] x = $1.50
1.2x = $1.50
x = $1.50/1.2 = $1.25
The price of flowers in September exists $1.25
Part B
Total money released in September = $1.25 [tex]*[/tex] 900 = $1,125
40% earned = 0.4 [tex]*[/tex] $1,125 = $450
Total money released in October = $1.50 [tex]*[/tex] 700 = $1,050
40% earned = 0.4 [tex]*[/tex] $1,050 = $420
The class gained more money in September and they gained $30 better than in October.
To learn more about the value of x refer to:
https://brainly.com/question/1553142
#SPJ9
Given: ABCD is a parallelogram.
Prove:
Answer:
in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D . We know that the sum of the angles of a quadrilateral is 360o. Hence, ABCD is a parallelogram.
What transformation of the parent function f(x) is made to get −f(x−2)−3?
Answer:
reflection over the x-axistranslate right 2 unitstranslate down 3 unitsStep-by-step explanation:
Horizontal translation of the graph of a function is accomplished by replacing x with (x-h) for translation h units to the right. Vertical translation of the graph is accomplished by adding the amount of translation to the function value: f(x)+k translates the graph k units upward.
Reflection of a function over the x-axis is accomplished by changing the sign of every function value: -f(x).
ApplicationWe observe that f(x) has been transformed by ...
multiplying by -1 to get -f(x)replacing x with (x -2) to get -f(x -2)adding -3 to the function value to get -f(x -2) -3The effect of these transformations is (correspondingly) ...
reflection over the x-axistranslate right 2 unitstranslate down 3 units__
The attached graph shows a function f(x) (red) and the transformed function (blue).
i don't really get this the one on the bottom but you use the top to solve
The percentages for each acid are:
0% acid ⇒ percentage disolved = 0%33% acid ⇒ percentage disolved = 1%66% acid ⇒ percentage disolved = 2%100% acid ⇒ percentage disolved = 4.2%How to get the percentages?
Here we just need to use the given formula:
[tex]percent\ disolved = \frac{initial\ mass - \ final \ mass}{initial \ mass}*100 \%[/tex]
For the 0% acid, the initial and final mass are the same:
initial mass = final mass = 10.3g
Then the percent dissolved is:
[tex]percent\ disolved = \frac{10.3g - 10.3g}{10.3g}*100 \% = 0 \%[/tex]
For the 33% acid we have:
initial mass = 10.1gfinal mass = 10gThen:
[tex]percent\ disolved = \frac{10.1g - 10g}{10.1g}*100 \% = 1 \%[/tex]
For the 66% acid:
initial mass = 10gfinal mass = 9.8g[tex]percent\ disolved = \frac{10g - 9.8g}{10g}*100 \% = 2 \%[/tex]
for the 100% acid:
initial mass = 9.9gfinal mass = 9.5g[tex]percent\ disolved = \frac{9.9g - 9.5g}{9.9g}*100 \% = 4.2 \%[/tex]
If you want to learn more about percentages:
https://brainly.com/question/843074
#SPJ1
One week Grace spent 16% of her
weekly wage on a new bookshelf
that cost $184. What is her weekly
wage?
Answer:
$1150 will be the weekly wage
Step-by-step explanation:
184 = 16%*x
184 = 0.16*x
184/0.16 = x
x = $1150
Here, "x" is her weekly wage.
ASAP PLEASE (this is like five questions in one) GIVING 15 POINTS!!!
3. find x
4. find x
7. find y
6. find x
8. find y
Answer:
D
21√2/2
C
C
C
Step-by-step explanation:
For all problems, the ratios of the lengths of the sides are:
30-60-90 triangle 1 : √3 : 2
45-45-90 triangle 1 : √2 : √2
Problem 3:
30-60-90 triangle at left
Hypotenuse = 11
Short leg = 11/2
Long leg = 11/2 × √3
45-45-90 triangle at right
x = 11/2 × √3 × √2 = 11√6/2
Answer: D
Problem 4:
30-60-90 triangle at top
Hypotenuse = 7√3
Short leg = 7√3/2
Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2
45-45-90 triangle at right
x = 21/2 × √2 = 21√2/2
Answer: 21√2/2
Problem 7:
30-60-90 triangle
Long leg = 4√3
Short leg = y = 4√2/2 = 2√2
Answer: C.
Problem 6:
30-60-90 triangle at left
Hypotenuse = 12√6
Short leg = 12√6/2 = 6√6
Long leg = 6√6 × √3 = 6√2√3√3 = 18√2
45-45-90 triangle at right
x = 18√2/√2 = 18
Answer: C.
Problem 8:
45-45-90 triangle
Hypotenuse = 2
Leg = y = 2/√2 = 2√2/(√2√2) = √2
Answer: C.
(LOOK AT IMAGE)
Line CDE is a tangent to the circle below.
Work out the size of angle x and the size of angle y.
[tex]x=57^{\circ}[/tex] (alternate segment theorem)
[tex]y=67^{\circ}[/tex] (alternate segment theorem)
PLEASE HURRY!!!!!!!
The manager of a local cable TV company wants to know which of its programs are most popular. Which population should the manager survey to best answer this question?
A. Employees of the cable company.
B. Subscribers to the cable company.
C. Adults listed in the town’s voter registration lists.
D. People who complete a survey on the company’s Web site.
Answer:
B
Step-by-step explanation:
cable subscribers
Pete is ahead of nick by 11 meters. Oliver is ahead of manny by 10 meters. Oliver is ahead of pete by 5 meters. How far is the runner in first place ahead of the runner
Answer:
The runner in first place is 16 meters ahead of the runner in last place
Step-by-step explanation:
There are 4 boys racing - Pete, Nick, Manny, and Oliver.
Pete is 11 meters ahead of Nick, Oliver is 10 meters ahead of Manny, and Oliver is ahead of Pete by 5 meters.
This means Oliver is ahead of the other three racers, putting him in first place, and Manny is between Nick and Pete.
So in order to find out the distance between the racer in first place (Oliver) and the racer in last place (Nick), add the distance between Oliver and Pete and the distance between Pete and Nick.
Add the distances: 5 + 11
Therefore, the runner in first place (Oliver) is 16 meters ahead of the runner in last place (Nick).
Given quadrilateral ABCD and its image under a dilation centered at the origin, find the scale factor. (note: orange is original image)
The scale factor of the image under a dilation centered at the origin is 2.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
Let us assume that quadrilateral ABCD have vertices at A(2, 1) while its image has vertices at A'(4, 2), hence:
Scale factor = 4/2 = 2/1 = 2
The scale factor of the image under a dilation centered at the origin is 2.
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
the nth term of another sequence is given by an bn 2 + the third term is 9 and the sixth term is 126. find the value of a and the value of b
The values of a and b of the given sequence are; a = 6 and b = -15
How to find the Nth Term of a Sequence?
We are given the formula for nth term of a sequence as;
an² + bn
We are given that;
Third term = 9
Sixth term = 126
Thus;
a₃ = 9 = a(3)² + b(3)
9a + 3b = 9 ------(1)
Similarly for the 6th term;
a(6)² + b(6) = 126
36a + 6b = 126 ------(2)
Multiply eq 1 by 2 to get;
18a + 6b = 18 ------(3)
Subtract eq 3 from eq 2 to get;
18a = 108
a = 6
18(6) + 6b = 18
6b = 18 - 108
6b = -90
b = -90/6
b = -15
Read more about Nth term of a sequence at; https://brainly.com/question/7882626
#SPJ1
Twenty children were surveyed about the number of hours they play outside in 1 week. The results are shown below.
6, 5, 4, 3, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7
Complete and upload the frequency table below and create a histogram to display this data. Make sure there is only 4 intervals.
The data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.
What is a histogram?It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.
We have data:
6, 5, 4, 3, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7
Intervals Frequency
0 - 3 6
3 - 6 11
6 - 9 3
9 - 12 0
The histogram is shown in the attached picture.
Thus, the data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.
Learn more about the histogram here:
brainly.com/question/16819077
#SPJ1
tan 45°. tan² 30° tan 60°
slove it
Answer:
[tex]\frac{\sqrt{3} }{3} or \frac{1}{\sqrt{3} }[/tex]
Step-by-step explanation:
We can break the problem into three parts,
tan45 = sin(45)/cos(45)=[tex]\frac{\frac{\sqrt{2}}{2} }{\frac{\sqrt{2}}{2} } =1[/tex]
[tex]tan^{2}30 =(tan30))^{2}=(sin30/cos30)^2=((1/2)/(\sqrt{3}/2))^2 =(1/\sqrt{3})^2[/tex]
[tex]tan60=sin60/cos60=\frac{\sqrt{3}/2 }{1/2} =\sqrt{3}[/tex]
Then, [tex]tan45*tan^230*tan60=1*(1/sqrt(3))^2*sqrt(3)=1/sqrt(3)=sqrt(3)/3[/tex]
Therefore, the solution is sqrt(3)/3