There are three possible solutions:
6 medium-sized candies and 4 small candies. 1 large candy, 3 medium-sized candies and 6 small candies. 2 large candies and 8 small candies.How to find possible solution from a system of equations whose number of variables is greater than the number of equations
Let be [tex]x[/tex], [tex]y[/tex] and [tex]z[/tex] the quantities of large, medium-sized and small candies bought by the unicorn., which represent non-negative integers. After a quick reading, we build the following system of linear equations:
[tex]x + y + z = 10[/tex] (1)
[tex]4\cdot x +2\cdot y +z = 16[/tex] (2)
We notice that the number of variables is greater than the number of linear equations. Thus, the system have several solutions. By (1):
[tex]z = 10 - x - y[/tex]
(1) in (2):
[tex]4\cdot x + 2\cdot y + 10 - x - y = 16[/tex]
[tex]3\cdot x + y = 6[/tex] (3)
After some inspections, we find three possible solutions:
[tex]x = 0[/tex], [tex]y = 6[/tex], [tex]z = 4[/tex][tex]x = 1[/tex], [tex]y = 3[/tex], [tex]z = 6[/tex][tex]x = 2[/tex], [tex]y = 0[/tex], [tex]z = 8[/tex]There are three possible solutions:
6 medium-sized candies and 4 small candies. 1 large candy, 3 medium-sized candies and 6 small candies. 2 large candies and 8 small candies.To learn more on systems of linear equations, we kindly invite to check this verified question: https://brainly.com/question/20379472
4x0.75
Expian pls
4x0.75
4/0.65
Answer:
3
Step-by-step explanation:
0.75 out of 1 for 4 is 3
for 4
0.25 is 1
0.5 is 2
0.75 is 3
1 is 4
4/0.65 = 2.15 (not 100% on this one)
(5x-25)(x+4)=0
What’s the answer
Answer:
x = - 4, x = 5
Step-by-step explanation:
(5x - 25)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
5x - 25 = 0 ⇒ 5x = 25 ⇒ x = 5
Answer:
x = - 4, x = 5
Step-by-step explanation:
(5x - 25)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
5x - 25 = 0 ⇒ 5x = 25 ⇒ x = 5
Hence, the correct answer is x=-4, x=5
Please find the perimeter and area of these shapes
Answer:
ABC shaded area = 36[tex]\pi[/tex] - 72 cm²
ABC shaded area perimeter = [tex]6\pi +12\sqrt{2}[/tex] cm
ABCD area = [tex]\dfrac52 \pi[/tex] cm²
ABCD perimeter = [tex]3\pi +2[/tex] cm
Step-by-step explanation:
Shape ABC
Assuming you want the area and perimeter of the shaded part of the shape only...
Area
Area of a sector = [tex]\dfrac12r^2\theta[/tex] (where r is the radius and [tex]\theta[/tex]
⇒ area of a sector = [tex]\dfrac12 \times 12^2\times \dfrac{\pi}{2} =36\pi \ \textsf{cm}^2[/tex]
Area of triangle = 1/2 x base x height
⇒ area of triangle = 1/2 x 12 x 12 = 72 cm²
Therefore, area of shaded area = area of sector - area of triangle
⇒ area = 36[tex]\pi[/tex] - 72 cm²
Perimeter
Arc length = [tex]r\theta[/tex] (where r is the radius and [tex]\theta[/tex]
⇒ arc length = [tex]12\times\dfrac12\pi =6\pi \ \textsf{cm}[/tex]
Hypotenuse of triangle = [tex]\sqrt{a^2+b^2}[/tex] (where a and b are the legs of the right triangle)
⇒ hypotenuse = [tex]\sqrt{12^2+12^2} =12\sqrt{2}[/tex] cm
Therefore, perimeter = arc length + hypotenuse
⇒ perimeter = [tex]6\pi +12\sqrt{2}[/tex] cm
Shape ABCD
Area
Area of a semicircle = [tex]\dfrac12 \pi r^2[/tex] (where r is the radius)
⇒ area of large semicircle ABC = [tex]\dfrac12 \times \pi \times 2^2=2\pi \ \textsf{cm}^2[/tex]
⇒ area of small semicircle AD = [tex]\dfrac12 \times \pi \times 1^2=\dfrac12\pi \ \textsf{cm}^2[/tex]
⇒ area of shape ABCD = [tex]\dfrac12 \pi + 2 \pi=\dfrac52 \pi \ \textsf{cm}^2[/tex]
Perimeter
1/2 circumference = [tex]\pi r[/tex]
⇒ perimeter = [tex]2\pi +2+\pi=3 \pi+2 \ \textsf{cm}[/tex]
There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?
Answer:
1/3 x 3/11 = 3/33 or 0.09, or 9 percent
Step-by-step explanation:
Answer:
16/144
4/12 × 4/12 = 16/144
A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 10^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 21^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance between points A and B and the boat is an illustration of elevation and distance
The distance from point A to point B is 346 feet
How to calculate the distance ABThe height of the lighthouse is given as:
h = 113
The distance between point A and the base of the lighthouse is calculated using the following tangent ratio
[tex]\tan(10) = \frac{113}{A}[/tex]
Make A, the subject
[tex]A = \frac{113}{\tan(10)}[/tex]
[tex]A = 640.85[/tex]
The distance between point B and the base of the lighthouse is calculated using the following tangent ratio
[tex]\tan(21) = \frac{113}{B}[/tex]
Make B, the subject
[tex]B= \frac{113}{\tan(21)}[/tex]
[tex]B= 294.38[/tex]
The distance AB, is then calculated as:
[tex]AB = A - B[/tex]
[tex]AB = 640.85 - 294.38[/tex]
[tex]AB = 346.47[/tex]
Approximate
[tex]AB = 346[/tex]
Hence, the distance from point A to point B is 346 feet
Read more about elevation and distance at:
https://brainly.com/question/7243416
Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
Choose two equations that can be used to find the height, h, of the tree. what is the equation
Answer:
the answer is... Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
Choose two equations that can be used to find the height, h, of the tree.
Step-by-step explanation:
hope it helps
The two equations that can be used to find the height are as follows:
12 / 4 = h /5
5 / 4 = h / 12
What is Similar Triangles?Similar triangles are not necessarily the same in size. Corresponding angles of similar triangles are congruent. The sides of similar triangle are a ratio of each other.
here, we have,
Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
The tree cast a shadow of 12 ft.
Let's establish the proportion base on similar triangles. The height of the tree is h.
Therefore,
h / 12 = 5 / 4
Therefore,
h / 12 = 5 / 4
cross multiply
4h = 60
divide both sides by 4
h = 60 / 4
h = 15 ft
Therefore, the two equations that can be used to find the height are as follows:
12 / 4 = h /5
5 / 4 = h / 12
learn more on similar triangles here:
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#SPJ7
How many eighth graders chose History as their favorite subject. Round answer to the nearest whole number.
19%
22%
27%
33%
The percentage of eighth-graders that chose History as their favorite subject is 19%
Percentages and proportionFrom the given table, we have the following parameters
Total students in the 8th grade = 124 students
Total number of 8th graders that chose history = 11 + 12
Total number of 8th graders that chose history = 23
Required percentage = 23/124 * 100
Required percentage = 19%
Hence the percentage of eighth-graders that chose History as their favorite subject is 19%
Learn more on percentages here: https://brainly.com/question/24304697
The triangles shown below must be congruent.
O True
O False
Answer:
The answer to the problem is True
Order he distance traveled from least to greatest
30 kph for 4 hours
5 kph for 10 hours
15 kph for 2 hours
35 kph for 1 hour
Answer:
15 for 2 = 30km
35 for 1 = 35km
5 for 10 = 50km
30 for 4 = 120km
Step-by-step explanation:
formula is
distance = speed x time
Exit Ticket: Solve the triangle.
Solve the following problem. Round to one decimal place if
necessary. If your answer is correct you will see an image
appear on your screen.
T
.
Х
35
45°
Х
The value of x from the figure is 35√2
SOH CAH TOA identityFrom the given figur, we have the following parameters
figure
Opposite = 35
Angle = 45 degrees
Required
Hypotenuse = x
USing the theorem
Sin 45 = 35/x
x = 35/sin45
x = 35√2
Hence the value of x from the figure is 35√2
Learn more on soh cah toa here; https://brainly.com/question/20734777
Below are two regular polygons. Calculate the value of angle a. a a
Answer:
12°
Step-by-step explanation:
The outer polygon is a hexagon and the inner polygon is a pentagon.
Let's start by finding the measure of an interior angle of the (regular) hexagon.
The sum of the measures in a polygon is:
(n-2)(180)
Where n represents the amount of sides in a figure therefore...
(6-2)(180)=4(180)=720
Then, we divide 720 by 6 (because there are 6 angles), to find the measure of one angle...
720/6=120
Next, find the measure of an interior angles of a (regular) pentagon.
(n-2)(180)=(5-2)(180)=3(180)=540
Divide 540 by 5 (there are 5 angles), to find the measure of one angle...
540/5=108
Now, subtract 120 by 108 to find a...
120-108=12
a=12°
Can you help with my math work please
Answer:
A. pen 0.75, pencil 0.50
Step-by-step explanation:
there is 4 of each that means you have to multiply by 4so
0.75 × 4 = 3
0.50 × 4 = 2
add them up equal 5
Answer:
The correct option is A. Pen $0.75; pencil, $0.50
given that €1 =£0.75
a how much is €530 in £
b £1 =€
Answer:
a) £397.50
b) £1 ≈ €1.33
Given:
€1 = £0.75
To find out:
a)
€530 = £0.75 × 530
€530 = £397.50
b)
Since £397.50 = €530:
£1 = €530 ÷ 397.5
£1 = €1.33333333333
£1 ≈ €1.33
A right angle has a greater measure than a(n) blank angle and a lesser measure than a(n) blank angle
Answer:
Step-by-step explanation:
The angle measure of a right angle is 90 degrees.
Acute angles are angles with measures less than 90 degrees.
Obtuse angles are angles with measures more than 90 degrees.
So,
A right angle has a greater measure than a(n) acute angle and a lesser measure than a(n) obtuse angle
A 6-pack of dish towels costs $21.36. What is the unit price?
Answer:
$3.56
Step-by-step explanation:
Divide 21.36 by 6 and you get 3.56
Answer:
d = $3.56
Step-by-step explanation:
d = the cost of each towel
6d = 21.36
/6 /6
d = $3.56
Check your answer:
6d = 21.36
6(3.56) = 21.36
21.36 = 21.36
Hope this helps!
If y = x3 + x,
find the value of y when x=-2
Answer:
y=-8
Step-by-step explanation:
if x=-2 -2*3= -6, -6+-2=-8
Answer:
-8
Step-by-step explanation:
-2 times 3 is -6, and -6 plus -2 equals -8
The following box plot shows points awarded to dance teams that competed at a recent competition:
box plot with number line titled Points with 0 as the minimum, 50 as quartile 1, 70 as the median, 90 as quartile 3, and 100 as the maximum
Which dot plot best represents the box plot data?
Answer:
The answer is A
Step-by-step explanation:
I Just took the test a couple hours ago, and i got it right :)
Answer:
Graph A.
Step-by-step explanation:
Given that this is a symetrical graph, the only symetrical graph is the following one: Graph A.
Plus, I got it right one the 05.01 Representing Data test.
Hope this helps!
PLEASE HELP ME PLEASE HELP ME I NEED HELP ON SIX PLEASE ANSWER ME AND DONT SEND LINKS THAT DONT WORK!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Pudge sold 8 tickets, Christi sold 19
tickets, Ace sold 38 tickets
Step-by-step explanation:
x = Pudge
3x - 5 Christi
2(3x-5) = Ace
Let x, 3x - 5 and 2(3x-5) be the tickets
x + (3x- 5) +2(3x - 5) = 65
Combine like terms
x+ (3x - 5) + 6x - 10 = 65
4x -5+6x - 10 = 65
10x - 5-10 = 65
Transpose -5 and -10 and change their
signs
10x = 65 +5+ 10
Add
10x = 80
Divide both sides by 10
10x/10x = 80/10
x =8
Pudge sold 8 tickets.
Evaluate x as 8
3x-5
3(8)-5
24-5 19
Christi sold 19 tickets.
2(3x-5)
2(3(3)- 5)
2(24- 5)
2(19)= 38
Ace sold 38 tickets.
Checking:
x+ (3x - 5) +2(3x - 5) = 65
8+(3(8)-5) +2(3(8) - 5) = 65
8 +19 +38 = 65
65 =65
Nolan drives 15 miles in 30 minutes. If he drove three hours in total at the same rate,
how far did he go?
Before you try that problem, answer the question below.
How many minutes did Nolan drive in total?
A cube has an edge length of 14 feet. What is its volume, in cubic feet?
Answer:
V=2744ft³ is the answer
Answer:
2,744 cubic feet
Step-by-step explanation:
You only need a single measurement, then you multiply it by itself and by itself again, equivalent to raising it to the power of 3. Finally, adjust the unit to its cubic equivalent. in this case Volume = (Edge of the cube) 3 so 14 x 14 x 14 is 2,744
irrational
This equivalent to 27 is
also in the 359th digit
position of Pi
F
The circumference of a circle is 360 degrees, and the number 360 is the 359th digit point of pi.
Hope that helps :)
how to simplify 8x+5x
Answer: 13x
Step-by-step explanation: Since 8x and 5x are like terms, we can add them together.
8x+5x=13x
Have a nice day! :)
I don't know this. Can someone please help me. I am in 7th grade.
Answer:
590 or 589.89
Step-by-step explanation:
Hope this helps!
Answer:
1380.25
Step-by-step explanation:
So to solve this problem, you find the outside circle and subtract it from the inside circle.
So, lets find the basic values
Radius of inside circle = diameter of the inside circle / 2
= 27.6
= 13.8
Radius of outside part = 11.3
So the area of the outside circle is
A = pi r^2
= pi (11.3 + 13.8)^2
= 630.01
= 1978.23
And the area of the inside circle is
A = pi r^2
= pi (13.8)^2
= 190.44
= 597.98
To find the shaded part, we subtract the outer circle with the inner circle
1978.23 - 597.98 = 1380.25
The area of the shaded region is 1380.25
Maritar has a
triangluar garden 17% of it in plantel corrests, what
area is planted with carrots...
Answer:
WRONG SUBJECT
Step-by-step explanation:
YOU'RE QUESTIOON WAS DELETED FOR THE WRONG SUBJECT
Find the geometric mean of 4 and 49
which of the following lists of ordered pairs is a function?
Answer:
A (Only A)
Step-by-step explanation:
the X position can NOT repeat itself at all. In A it does not do that but in the rest it does
in B there is a 2,5 and a 2,2 (Repeating X)
in C there is a -1,4 and a -1, 7 (Repeating X)
in D there is a 3,1 and a 3,2 (Repeating X)
Answer:
A
Step-by-step explanation:
A function is a set of coordinate points that has a separate point for the x axis in every pair.
In order to find a function, just look at the first number in every parentheses and see if there are any multiples
Answer A has -2, 2, -3, and 3
Answer B has 2, 3, 4, and 2
Answer C has 0, -1, 1, and -1
Answer D has 1, 2, 3, and 3
Answer A is the only one that doesn't have repeating x points
Please give brainliest if I helped! :)
Normal Samantha is using ribbon to make bows to be sold at a school fundraiser. She has 83.2 meters of ribbon. She needs 1.28 meters of ribbon for each bow. How many bows she can make?
The answer would be 65
hope that helps :b
Answer:
83.2 meters ÷ 1.28 meters = 65 bows
Can someone please help me with this ty!
please help fast i have 30 mins
Which of these is an example of an overdraft?
A. Having $517.98 in your checking account and writing a check for
$563.28
B. Having $322.15 in your checking account and writing a check for
$298.67
C. Having $133.74 in your checking account and writing a check for
$118.55
D. Having $485.39 in your checking account and writing a check for
$479.43
Why nobody had this
Answer:
So its A.
Step-by-step explanation:
For future ppl if they need it :)