Answer: [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
Step-by-step explanation:
General equation of ellipse : [tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}[/tex]
Given: Vertices of ellipse : (± 9,0)
Since the vertices are of the form (± a, 0).
i.e. a=9
Thus, the major axis is along x-axis.
Also, foci of the ellipse = (±5,0)
Since, foci is of the form (± c,0), i.e. c=5
Since
[tex]c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56[/tex]
Equation of ellipse :
[tex]\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
Hence, the required equation : [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
There are 5 oranges, three apples, 12 grapes, and 2 avocados in the fruit basket of Ms. Canton's refrigerator. Write a ratio of grapes compared to all of the fruit.
Answer:
6:11
Step-by-step explanation:
There are 12 grapes and 12 + 5 + 2 + 3 = 22 total fruits, so the ratio is 12:22 which simplifies to 6:11.
Step-by-step explanation:
Given:
Orange=5
Apple=3
Grape=12
Avocado=2
Formula:
Grape:Fruits
Answer:
Fruits= 5+3+12+2
Fruits=22
Grape/Avocado
12/2=6
Grape:Apple
12/3=4
Grape:Orange
12/5=2.4
Grape: All fruits
12/22=0.54
Hope it helps ;) ❤❤❤
HELPHELOHELPJRJRKTJTJT HELP PLS
Answer:
1: 18
2: P
Step-by-step explanation:
1: each number in the second row is the square of the number in the first row but it's kinda backwards! for example 4×4=16 writing it backwards would be 61.
now: 9×9=81 and the backwards would be 18
2:the code for each letter is the number of its ends! like: A has 2 ends. S has 2 Ends. O doesn't have any ends.
now: the only letter left with 1 end is P
Answer: pretty tricky question, the answer would be 18
Step-by-step explanation:
each number is multiplied by itself so
4x4=16
and then reverse the writing of the product
16 to 61
9x9=81
81 to 18
help me plz i need help
Answer:
i think its the first one-
Step-by-step explanation:
Answer:
the answer is the second one to the right on the top.
Step-by-step explanation:
i got it right on the quiz
Copy the problems on paper, mark the givens, and fill in the blanks to complete the proofs of the statements asked.
You didn't attach a photo, so I am confused on what your question is. I am answering 3 problems that have the same intro.
If your question was not any of these, I can't help, sorry :)
HELP FIRST GET BRAINLLEST Measure the difference between the lower quartile of Data Set A and the lower quartile of Data Set B. Round to the nearest tenth when performing all operations.
Answer:
29
Step-by-step explanation:
To find the lower quartile you need to split it into 2 by finding the median
Set A: 73, 75, 79, 81, 84, 85
Set B: 47, 49, 51, 51, 55, 56
Now you have to find the median of each
A: 80
B: 51
Lastly, you subtract and get 29
What is the volume of the following rectangular prism?
Answer:
Step-by-step explanation:
The Volume is given by the following equation: V= Base x Height
Therefore, [tex]V = 16\frac{1}{4} * \frac{1}{2} = \frac{65}{4} * \frac{1}{2} = \frac{65}{8} = 8\frac{1}{8}[/tex] units
Destiny and Guadalupe are shopping. Destiny buys 2 pairs of pants and 6 bracelets and pays $178.Guadalupe buys 3 pairs of pants and 2 bracelets and pays $155. Solve for the price of each item.
For the entirety of this problem, p will represent a pair of pants and b will represent a bracelet.
Step 1) Set up equations for Destiny and Guadalupe
Destiny: 178 = 2p + 6b
Guadalupe: 155 = 3p + 2b
I will be using substitution to solve this problem, but elimination can also be used.
Step 2) Solve Destiny's equation for p
178 = 2p + 6b
178 - 6b = 2p
89 - 3b = p
Step 3) Substitute the found value of p from Destiny's equation into Guadalupe's equation and solve for b
155 = 3(89 - 3b) + 2b
155 = 267 - 9b + 2b
155 = 267 - 7b
-7b = -112
b = 16
Step 4) Use the value of b found in step 3, plug that back into our equation from step 2 and solve for p
89 - 3(16) = p
89 - 48 = p
p = 41
one pair of pants = $16
one bracelet = $41
Hope this helps!! :)
A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove that two triangles are conjurent. For each pair of triangles, select the correct statement.
Answer:
The answer is given below
Step-by-step explanation:
The statements are not given but from this definition, you should be able to select the correct statement.
Triangles are said to be congruent if they have the same size and shape. A triangle is made up of six (three sides and three angles) but only three is usually needed to prove triangle congruence. These are:
a) Side - Side - Side (SSS): Two triangles are congruent if the length of their three sides are equal to each other.
b) Side- angle- side (SAS): If two sides and one angle of a triangle is equal to two sides and a angle of another triangle then the two triangles are congruent to each other.
c) Angle - side - angle (ASA): If two angles and a side of a triangle are equal to a corresponding two angles and a side of another triangle then the two triangles are congruenr.
d) Right angle - hypotenuse - side (RHS): If for two right angled triangles, their hypotenuse and a side (leg) are equal, then the two triangles are congruent.
✖️-101 2 3 f(✖️) -2-1 -1/2-1/4-1/8 -9/4 -7/12 12/7 7/12 Given the following table,fine the rate of change between f(-1) and f(2).
Answer: [tex]\frac{7}{12}.[/tex]
Step-by-step explanation:
Given table:
X f(X)
-1 -2
0 -1
1 [tex]-\dfrac{1}{2}[/tex]
2 [tex]-\dfrac{1}{4}[/tex]
3 [tex]-\dfrac{1}{8}[/tex]
i.e. , f(-1) = -2
f(2) = [tex]-\dfrac{1}{4}[/tex]
The rate of change between [tex]f(a)[/tex] and [tex]f(b)=\dfrac{f(b)-f(a)}{b-a}[/tex]
Then, the rate of change between f(-1) and f(2) = [tex]\dfrac{-\dfrac{1}{4}-(-2)}{2-(-1)}[/tex]
[tex]=\dfrac{-\dfrac{1}{4}+2}{3}=\dfrac{\dfrac{-1+8}{4}}{3}\\\\=\dfrac{\dfrac{7}{4}}{3}\\\\=\dfrac{7}{12}[/tex]
Hence, the rate of change between f(-1) and f(2) is [tex]\frac{7}{12}.[/tex]
Find the value of x in the triangle shown below.
Answer:
The valueof x is root under 41.
Hope this helps.
A golfer attempts to hit a golf ball over a valley from a platform above the groun
The functions that models the height of the ball is h(t) = -5t2 + 40t + 100
where h(t) is the height in metres at time t seconds after contact. There are
power lines 185 metres above the ground. Will the golf ball hit power lines?
Answer: NO
Step-by-step explanation:
The functions that models the height of the ball is given as
h(t) = -5t2 + 40t + 100
Where
a = -5, b = 40, c = 100
The time the ball will reach the maximum height will be the vertex of the parabola. At the line of symmetry, the time t will be:
t = -b/2a
Substitute b and a into the formula above.
t = - 40 / -5 = 8
Substitute 8 for t in the function f(t)
h(t) = - 5(8)^2 + 40(8) + 100
h(t) = -5(64) + 40(8) + 100
Open the bracket
h(t) = -320 + 320 + 100
h(t) = 100
The maximum height of the ball is 100m
Given that the power lines is 185 metres above the ground. The golf ball will therefore not hit power lines because the maximum height the ball can go is 100 metres
3 sides of the triangle are distinct prime numbers. What is the smallest possible perimeter of the triangle?
Answer:
the smallest possible perimeter is 6
Step-by-step explanation:
since the smallest possible prime number is 2 it would make since if each side is 2 which makes the smallest perimeter possible. i really hope this helped :)
Answer:
6
Step-by-step explanation:
the smallest possible number will be 2.
2 inches/centimeters of each 3 sides of the triangle
PLEASE HELP ASAP. IT'S TIMED. If your quadratic equation had no numbers and was represented by ax²+bx=c. Tell me step by step what I should do to complete the square. PLEASE HELP ASAP.
Answer:
(x+ (b/2a))^ 2 = (b/2a) ^2 + c/a
Step-by-step explanation:
ax²+bx=c
first we know the form of a square
(x+a)^2 = x^2 + 2ax + a^2
we have to write the given ax²+bx=c in the above form
for that we bring c on LHS
for the we subtract c from both sides
ax²+bx -c =c - c
=> ax²+bx - c = 0
now we see that in x^2 + 2ax + a^2 , term x^2 does not have any coefficient,
so in our equation we get rid of coefficient a from ax²+bx - c = 0
for that we divide both LHS and RHS by a
(ax²+bx - c)/a = 0/a
x²+bx/a - c/a = 0
now we have to write (b/a)x in form of 2ax
for we divide and multiply (b/a)x by 2
thus we have
x²+2 (b/2a)x - c/a = 0
now comparing above equation with x^2 + 2ax + a^2
we see that 2ax is same 2 (b/2a)x
thus (b/2a) is same as a in standard form of quadratic equation x^2 + 2ax + a^2
now we have to get a^2
as (b/2a) is same as a
we add and subtract square of (b/2a) on LHS
x²+2 (b/2a)x - c/a + (b/2a) ^2 - (b/2a) ^2 = 0
rearranging it
x²+2 (b/2a)x + (b/2a) ^2 - (b/2a) ^2 -c/a = 0
=> x^2 + (b/2a)x + (b/2a) ^2 -(b/2a) ^2 -c/a = 0
=> (x+ (b/2a))^ 2 - ((b/2a) ^2 + c/a ) = 0
=> (x+ (b/2a))^ 2 = (b/2a) ^2 + c/a answer
Find the unknown angle measure. A -50° b - 180° c - 220° d - 40°
Answer:
40 degrees
Step-by-step explanation:
90 degrees + 50 degrees = 140 degrees
there are 3 angles that total at 180 degrees in every triangle
180 degrees - 140 degrees = 40 degrees
f(X) x-2/2 find FF(X)
[tex]f(x) = \dfrac{x-2}{2}\\\\\\f(f(x)) = \dfrac{\dfrac{x-2}{2}-2}{2}\\\\\\f(f(x)) = \dfrac{\dfrac{x-2-4}{2}}{2}\\\\\\f(f(x)) = \dfrac{x-6}{4}[/tex]
Write the first four terms in the following sequences. A(n+1)=A(n)−5 for n≥1 and A(1)=9 .
Answer:
Step-by-step explanation:
A(1) = 9
A(n+1) = A(n) - 5
n = 1 ; A(1+1) = A(1) - 5
A(2) = 9 - 5
A(2) = 4
n = 2 ; A(2+1) = A(2) - 5
A(3) = 4 - 5
A(3) = 1
n = 3 ; A(3+1) = A(3) - 5
A(4) = 1 - 5
A(4) = -4
n = 4 ; A(4+1) = A(4) - 5
A(5) = -4 - 5
A(5) = -9
First four terms are: 9 , 4 , 1 , -4 , - 9
Which of the following equations is of a parabola with a vertex at (0, 6)?
O y= (x - 6)2
O y= (x + 6)2
O y=x2-6
Oy= x2 + 6
Answer:
y= x^2 + 6
Step-by-step explanation:
y= x2 + 6 (which should be written as y= x^2 + 6) has the form y - k = a(x - h)^2. For y= x^2 + 6, h = 0 and k = 6. Thus the vertex is (0, 6)
A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqrt{10}$ with $a$ and $b$ integers. What is the sum of $a$ and $b$?
Answer:
a + b = 12
Step-by-step explanation:
Given
Quadrilateral;
Vertices of (0,1), (3,4) (4,3) and (3,0)
[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]
Required
[tex]a + b[/tex]
Let the vertices be represented with A,B,C,D such as
A = (0,1); B = (3,4); C = (4,3) and D = (3,0)
To calculate the actual perimeter, we need to first calculate the distance between the points;
Such that:
AB represents distance between point A and B
BC represents distance between point B and C
CD represents distance between point C and D
DA represents distance between point D and A
Calculating AB
Here, we consider A = (0,1); B = (3,4);
Distance is calculated as;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex](x_1,y_1) = A(0,1)[/tex]
[tex](x_2,y_2) = B(3,4)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]
[tex]AB = \sqrt{( - 3)^2 + (-3)^2}[/tex]
[tex]AB = \sqrt{9+ 9}[/tex]
[tex]AB = \sqrt{18}[/tex]
[tex]AB = \sqrt{9*2}[/tex]
[tex]AB = \sqrt{9}*\sqrt{2}[/tex]
[tex]AB = 3\sqrt{2}[/tex]
Calculating BC
Here, we consider B = (3,4); C = (4,3)
Here,
[tex](x_1,y_1) = B (3,4)[/tex]
[tex](x_2,y_2) = C(4,3)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}[/tex]
[tex]BC = \sqrt{(-1)^2 + (1)^2}[/tex]
[tex]BC = \sqrt{1 + 1}[/tex]
[tex]BC = \sqrt{2}[/tex]
Calculating CD
Here, we consider C = (4,3); D = (3,0)
Here,
[tex](x_1,y_1) = C(4,3)[/tex]
[tex](x_2,y_2) = D (3,0)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]
[tex]CD = \sqrt{(1)^2 + (3)^2}[/tex]
[tex]CD = \sqrt{1 + 9}[/tex]
[tex]CD = \sqrt{10}[/tex]
Lastly;
Calculating DA
Here, we consider C = (4,3); D = (3,0)
Here,
[tex](x_1,y_1) = D (3,0)[/tex]
[tex](x_2,y_2) = A (0,1)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]
[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]
[tex]DA = \sqrt{9 + 1}[/tex]
[tex]DA = \sqrt{10}[/tex]
The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral
[tex]Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}[/tex]
[tex]Perimeter = 4\sqrt{2} + 2\sqrt{10}[/tex]
Recall that
[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]
This implies that
[tex]a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}[/tex]
By comparison
[tex]a\sqrt{2} = 4\sqrt{2}[/tex]
Divide both sides by [tex]\sqrt{2}[/tex]
[tex]a = 4[/tex]
By comparison
[tex]b\sqrt{10} = 2\sqrt{10}[/tex]
Divide both sides by [tex]\sqrt{10}[/tex]
[tex]b = 2[/tex]
Hence,
a + b = 2 + 10
a + b = 12
Answer:
a+b=6
Step-by-step explanation:
The tutor verified answer is mostly correct however, if you look under both by comperision sections you will see that it is:
[tex]4\sqrt{2}[/tex] and [tex]2\sqrt{10}[/tex] thus the answer is 4+2=6
A certain clock is losing time. The clock loses 2/15 seconds every minute. How many seconds does the clock lose in one hour?
Answer:
8mins
Step-by-step explanation:
(2x60)/15=8 I hope this helps, hope it's right
Answer:
8 minutes
Step-by-step explanation:
You will multiply 60 times 2 and then divide by 15 leaving you with 8
About how much money would 18 pounds of cheese cost if the price is $3.95 per pound? Use two different ways to estimate the product. Are your estimates overestimate or underestimate? Explain.
1. this way is overestimating
assume that you are getting 20 pounds of cheese. that is 2 tens. so multiply 3.95 by 10 = 39.5 thats the price for 10 pounds of cheese. Since we're estimating to get 20 pounds, multiply by two or add 39.5 together twice. 79 dollars this is overestimating since you're raising the amount of cheese you're buying by 2 pounds
2. his way is overestimating
assume its 4 dollars per pound. 18*4 would be 10*4 + 8*4= 40+32 = 72 dollar
this is overestimating because you're raising the price of the cheese by 5 cents.
Answer: 71.1
Step-by-step explanation: Its really simple actully so what you do is you take 3.95 and you mulitply is by 18 or you can add 3.95 plus 3.95 18 times and you get drum roll please 71.1$. I hope my answer was help ful
Kobi and I need to know which of the following is NOT a possible value for the number of pennies
Answer:
A. 85
Step-by-step explanation:
SInce nickels are worth 5 cents, the number of pennies must end with an 8 or a 3 in order for the total to end with a 3 ($9.83)
Triangle RST was dilated with the origin as the center of dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The lengths of the sides of triangle RST are given. Enter the lengths of the sides of triangle R'S'T' below. (Decimal values may be used.) (yo idc about who answers it first, just get it right and I'll mark brainliest
Answer:
[tex]R' = 6[/tex]
[tex]S' = 7.5[/tex]
[tex]T' = 9[/tex]
Step-by-step explanation:
The question is incomplete; however the sides of the triangle are;
[tex]R = 8[/tex]
[tex]S = 10[/tex]
[tex]T = 12[/tex]
[tex]Scale\ Factor = \frac{3}{4}[/tex]
Required
Determine the sides of R'S'T'
The new sides of the triangle is calculated as thus;
[tex]New\ Side = Old\ Side * Scale\ Factor[/tex]
Calculating R'
[tex]R' = R * Scale Factor[/tex]
Substitute 8 for R and 3/4 for Scale Factor
[tex]R' = 8 * \frac{3}{4}[/tex]
[tex]R' = \frac{24}{4}[/tex]
[tex]R' = 6[/tex]
Calculating S'
[tex]S' = S * Scale Factor[/tex]
Substitute 8 for R and 3/4 for Scale Factor
[tex]S' = 10 * \frac{3}{4}[/tex]
[tex]S' = \frac{30}{4}[/tex]
[tex]S' = 7.5[/tex]
Calculating T'
[tex]T' = T * Scale Factor[/tex]
Substitute 8 for R and 3/4 for Scale Factor
[tex]T' = 12 * \frac{3}{4}[/tex]
[tex]T' = \frac{36}{4}[/tex]
[tex]T' = 9[/tex]
Triangle RST was dilated with the origin as the center of the dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The lengths of the sides of the triangle RST are given. Enter the lengths of the sides of the triangle R'S'T' below.
Answer:
6
7.5
9
PLEASE HURRY write the equation of the inverse function y=1/2cos^-1(pix)-3
Answer:
[tex]f^{-1}(x) = \frac{cos(2x+6)}{\pi }[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{2} cos^{-1} (\pi x)-3[/tex]
Firstly, we've to interchange the variables.
[tex]x = \frac{1}{2} cos^{-1}(\pi y)-3[/tex]
Solving for y
[tex]x = \frac{cos^{-1} \pi y}{2} -3[/tex]
Adding 3 to both sides
[tex]x+3 = \frac{cos^{-1}(\pi y)}{2}[/tex]
Multiplying 2 to both sides
[tex]2(x+3) = cos^{-1} (\pi y)\\2x+6 = cos^{-1} (\pi y)[/tex]
Taking cosine on both sides
[tex]\pi y = cos (2x+6)[/tex]
Dividing both sides by y
[tex]y = \frac{cos(2x+6)}{\pi }[/tex]
Replace y by [tex]f^{-1}(x)[/tex]
=> [tex]f^{-1}(x) = \frac{cos(2x+6)}{\pi }[/tex]
Answer:
[tex]\large \boxed{f^{-1}(x)=\frac{cos(2x+6)}{\pi} }[/tex]
Step-by-step explanation:
[tex]\displaystyle y=\frac{cos^{-1} (\pi x)}{2} -3[/tex]
Swicth variables.
[tex]\displaystyle x=\frac{cos^{-1} (\pi y)}{2} -3[/tex]
Solve for y.
Add 3 to both sides.
[tex]\displaystyle x+3=\frac{cos^{-1} (\pi y)}{2}[/tex]
Multiply both sides by 2.
[tex]\displaystyle 2(x+3)=cos^{-1} (\pi y)[/tex]
[tex]\displaystyle 2x+6=cos^{-1} (\pi y)[/tex]
Take the cos of both sides.
[tex]\displaystyle cos(2x+6)=\pi y[/tex]
Divide both sides by [tex]\pi[/tex].
[tex]\displaystyle \frac{cos(2x+6)}{\pi} =y[/tex]
Yolanda's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Yolanda $5.20 per pound, and type B coffee costs $4.05 per
pound. This month, Yolanda made 130 pounds of the blend, for a total cost of $586.30. How many pounds of type B coffee did she use?
Answer:
78 pounds
Step-by-step explanation:
Let's say Yolanda makes a pounds of Type A coffee and b pounds of Type B coffee. Since the total number of pounds is 130, we can write the equation:
a + b = 130
We know the cost of Type A coffee is $5.20/lb and the cost of Type B coffee is $4.05/lb, so since the total cost is $586.30, we can write:
5.20a + 4.05b = 586.30
We can now solve the system of equations:
a + b = 130
5.20a + 4.05b = 586.30
Manipulate the first equation by subtracting b from both sides:
a + b = 130
a = 130 - b
Substitute 130 - b for a in the second equation:
5.20a + 4.05b = 586.30
5.20 * (130 - b) + 4.05b = 586.30
676 - 5.20b + 4.05b = 586.30
Move the terms with b to one side:
1.15b = 89.70
b = 78
Thus, Yolanda used 78 pounds of Type B coffee.
~ an aesthetics lover
The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, sold by the company: Part A: What
Answer:
dollars
Step-by-step explanation:
suppose a triangle has sides 3,4,and 6. Which of the following must be true?
Answer:
its not a right triangle
Step-by-step explanation:
(Algebra 1) The swim team is selling sweatshirts and towels to raise money for a trip to Mexico. The Coach asked the team to raise
at least $1000
The coach asked the team members how many towels and sweatshirts they would need to sell to meet their goal. The
sweatshirts cost $20.00 and the towels cost $15.
Joanne was trying to determine how to pre-order the items to promote the products. Choose the combinations of
sweatshirts and towels that would reach their goal.
Sweatshirts
Towel =
(s, t) = combinations
Select one or more:
a. (37.18)
b.(41.11)
C. (22,38)
d. (8,55
e. (13,51)
The solution to the inequality equations are Option A, Option C, Option E.
The ordered pairs are ( 37 , 18 ) , ( 22 , 38 ) and ( 13 , 51 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Let the number of sweatshirt = s
Let the number of towels be = t
Let the cost of one sweatshirt = $ 20.00
Let the cost of one towel = $ 15.00
The Coach asked the team to raise at least $1000
So , the value of 20s + 15t ≥ 1000
Now , substituting the values for s and t in the equation , we get
a)
The ordered pair to the solution of equation ( s , t ) = ( 37 , 18 )
So , 20s + 15t ≥ 1000 be equation (1)
Substituting the values for s and t in the equation , we get
20 ( 37 ) + 15 ( 18 ) ≥ 1000
740 + 270 ≥ 1000
1010 ≥ 1000
So , the inequality equation satisfies
b)
The ordered pair to the solution of equation ( s , t ) = ( 41 , 11 )
So , 20s + 15t ≥ 1000 be equation (1)
Substituting the values for s and t in the equation , we get
20 ( 41 ) + 15 ( 11 ) ≥ 1000
820 + 165 ≥ 1000
985 < 1000
So , the inequality equation does not satisfies
c)
The ordered pair to the solution of equation ( s , t ) = ( 22 , 38 )
So , 20s + 15t ≥ 1000 be equation (1)
Substituting the values for s and t in the equation , we get
20 ( 22 ) + 15 ( 38 ) ≥ 1000
440 + 570 ≥ 1000
1010 ≥ 1000
So , the inequality equation satisfies
d)
The ordered pair to the solution of equation ( s , t ) = ( 8 , 55 )
So , 20s + 15t ≥ 1000 be equation (1)
Substituting the values for s and t in the equation , we get
20 ( 8 ) + 15 ( 55 ) ≥ 1000
160 + 825 ≥ 1000
985 < 1000
So , the inequality equation does not satisfies
e)
The ordered pair to the solution of equation ( s , t ) = ( 13 , 51 )
So , 20s + 15t ≥ 1000 be equation (1)
Substituting the values for s and t in the equation , we get
20 ( 13 ) + 15 ( 51 ) ≥ 1000
260 + 765 ≥ 1000
1025 ≥ 1000
So , the inequality equation satisfies
Hence , the inequality equations are solved
To learn more about inequality equations click :
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Which number is an irrational number?
Answer:
[tex]\boxed{\sqrt[3]{16} }[/tex]
Step-by-step explanation:
=> [tex]\sqrt[3]{16}[/tex] is an irrational number because it cannot be written as the form [tex]\frac{p}{q}[/tex] which is the basic requirement of being a rational number.
=> [tex]\sqrt{100}[/tex] = 10 (A rational number because it's a whole number)
=> 1/8 (Rational as it is in the form p/q)
=> -2.2675 (Rational because it is an integer)
Answer:
[tex]\boxed{\sqrt[3]{16} }[/tex]
Step-by-step explanation:
An irrational number cannot be expressed in the form p/q, where p and q are whole integers.
[tex]\sqrt{100} =10[/tex]
[tex]\frac{1}{8} =0.125[/tex]
[tex]-2.2675= - \frac{907}{400}[/tex]
[tex]\sqrt[3]{16} \approx 2.51984209979... \neq \frac{p}{q}[/tex]
[tex]\sqrt[3]{16}[/tex] is an irrational number.
Draw a picture to help you find the answers.
When Andrew got in his car to drive home from work, be saw that his fuel gauge
indicated that the tank was1/2 full. When he pulled into his driveway, the fuel gauge
showed that he used 1/3 of the fuel that was in the tank before he started his trip home.
3) How full was the tank when Andrew arrived home?
4) If the fuel tank had 4 gallons of gasoline left when he got home, how many
gallons of gasoline can the fuel tank hold?
Answer:
2/6 (1/3)
12 gallons
Step-by-step explanation:
3) 1/2x1/3=1/6, so he'd used 1/6 of a tank.
1/2-1/6=
3/6-1/6=2/6. So the tank was 2/6 full, or 1/3 full when he got home.
4) If it's 1/3 full and has 4 gallons, it can hold 12 gallons. (4x3)
pls asap its not 128......In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer:
hope it helps
this is my best
please tell me if I'm wrong