Answer:
x = 1 and y = -8x
Step-by-step explanation:
Answer:
{y,x} = {-8,1}
Step-by-step explanation:
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = -8x
// Plug this in for variable y in equation [1]
[1] (-8x) - 6x = -14
[1] - 14x = -14
// Solve equation [1] for the variable x
[1] 14x = 14
[1] x = 1
// By now we know this much :
y = -8x
x = 1
// Use the x value to solve for y
y = -8(1) = -8
Solution :
{y,x} = {-8,1}
evaluate 1/3 m - 1 - 1/2 n when m = 21 and n = 12
Answer:
0
Step-by-step explanation:
1/3(21)-1-1/2(12)
7-1-6=6-6=0
What’s an exponential equation
Answer:
An exponential equation is when we let the the independent variable become the exponent.
Sue makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 1:4. Yellow paint is sold in 5 litre tins and each tin of yellow paint costs £38. Blue paint is sold in 10 litre tins and each tin of blue paint costs £58. Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin. Work out Sue's percentage profit on each tin of green paint she sells.
Answer:
Sue's percentage profit = 9% on each tin of green paint she sells.
Step-by-step explanation:
Litres of green paints mixed = 50 litres
Ratio of litres of yellow paint and litres of blue paint = 1:4.
To determine the litres of yellow paint, we say:
[tex]yellow \: paint = \frac{1}{4} \times 50 = 10 \: litres[/tex]
To determine the litres of blue paint, we say:
[tex]blue \: paint = \frac{4}{5} \times 50 = 40 \: litres[/tex]
Since yellow paint is sold in 5 litres per tin and each tin cost £38; she has 10 litres of yellow paint in all. That implies that she has 10/5 = 2 tin of yellow paint. If one tin cost £38; 2 tin cost 2 × £38 = £76
Similarly,
Since blue paint is sold in 10 litres per tin and each tin cost £58; she has 40 litres of blue paint in all. That implies that she has 40/10 = 4 tin of blue paint. If one tin cost £58; 4 tin cost 4 × £58 = £232
Total cost of yellow and blue paints = £232 + £76
= £308
Since Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin and she has 50 litres in all; we say: 50/10 litres = 5 tins = 5 × £89.32 = £446.60.
Thus, selling price of the green paint = £446.60
[tex]profit \: \% = \frac{selling \: price - cost \: price}{cost \: price} \times \frac{100}{1} [/tex]
[tex]profit \: \% = \frac{446.60 - 308}{308} \times \frac{100}{1} [/tex]
[tex]profit \: \% = \frac{138.60}{308} \times \frac{100}{1} [/tex]
[tex]profit \: \% = 0.45 \times 100[/tex]
[tex]profit \: \% = 45\%[/tex]
Sue's percentage profit for selling all the tins of green paint is 45%, having sold 5 tins. Therefore, Sue's percentage profit for selling each of the paint will be:
[tex]profit \: \% \: on \: each \: green \: tin = \frac{45}{5} = 9\%[/tex]
Hence, Sue's percentage profit for selling each tin of green paint is 9%.
Proof
9% × 5 tins of green paint = 45%
Final answer:
Sue's percentage profit on each tin of green paint she sells is approximately 44.94%. This is calculated by finding the total cost of inputs, subtracting from the total sales revenue, and then finding the profit ratio to the cost.
Explanation:
To calculate Sue's percentage profit on each tin of green paint she sells, we need to first determine the cost of producing the green paint and then subtract that cost from the selling price. The green paint is produced in a ratio of 1:4 yellow to blue paint, making 50 litres total. Therefore, Sue uses 10 litres of yellow paint and 40 litres of blue paint to make 50 litres of green paint.
Yellow paint costs £38 for a 5-litre tin, so two tins are needed (costing £76 total) to get the required 10 litres. Blue paint costs £58 for a 10-litre tin, so four tins are needed (costing £232 total) to get 40 litres. This brings the total cost to £308 for 50 litres of green paint.
Sue sells her green paint at £89.32 per 10-litre tin. Therefore, for 50 litres, she gets 5 tins x £89.32 = £446.60.
The profit Sue makes is the selling price minus the cost price, which is £446.60 - £308 = £138.60. To find the percentage profit per tin, divide the profit by the cost and multiply by 100:
(£138.60 / £308) x 100 = 44.94%
Therefore, Sue's percentage profit on each tin of green paint she sells is approximately 44.94%.
What is a 3-dimensional shape made of two identical circles connected by a rectangle
Answer:
cylinder
Step-by-step explanation:
Wendy kept track of the number of text messages she sent each day for three weeks. Drag and drop each number into the boxes to complete the frequency table .
Answer:
0-9 = 4
10-19 = 3
20-29 = 9
30-39 = 5
Step-by-step explanation:
I just did it right now!
The correct number into the boxes to complete the frequency table are,
Interval Frequency
0-9 4
10-19 3
20-29 9
30-39 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Wendy kept track of the number of text messages she sent each day for three weeks.
Now, We can formulate;
Interval Frequency
0-9 4
10-19 3
20-29 9
30-39 5
Thus, The correct number into the boxes to complete the frequency table are,
Interval Frequency
0-9 4
10-19 3
20-29 9
30-39 5
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12. Raymond is reading a road map. On the map,- inch represents 12 miles. Approximately
how many miles apart are two cities that are 3- inches apart on Raymond's map?
F. 12
G. 48
H. 96
J. 132
168
Answer:
168miles
Corrected question;
12. Raymond is reading a road map. On the map, 1/4- inch represents 12 miles. Approximately
how many miles apart are two cities that are 3 1/2 - inches apart on Raymond's map?
F. 12
G. 48
H. 96
J. 132
K .168
Step-by-step explanation:
Given;
1/4 inch = 12 miles
3 1/2 = 7/2 = 14/4 inch
number of 1/4 inch in 14/4 inch is;
14/4 ÷ 1/4 = 14
14/4 inch = 12×14 miles = 168miles
At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?
A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
Answer:
C
Step-by-step explanation:
V(t) = [x(t)]³
A(t) = 6[x(t)]²
dV/dt = k × 6[x(t)]²
Where k < 0
From the options,
taking k = -0.2
dV/dt = -1.2[x(t)]²
The correct answer is A) dV/dt=-1.2x^2, which represents a rate of volume decrease directly proportional to the cube's surface area.
Explanation:The question involves finding a differential equation that describes the rate at which the volume of a cube decreases when the rate is proportional to the cube's surface area. Since the surface area of a cube is 6x(t)^2 and the volume is x(t)^3, the rate of decrease in volume, dV/dt, is proportional to the surface area.
The correct differential equation would show this relationship by having the change in volume be proportional to the square of the edge length, so dV/dt = -kx^2 for some constant k, which means the valid option is A) dV/dt=-1.2x^2.
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Gretchen and her friend Hayley bought three bags of apples and three bunches of bananas from the fruit vendor. Gretchen and Hayley want to find the total number of pieces of fruit that they bought. Gretchen thinks she should multiply 3 by the number of apples in each bag, x, and add it to 3 times the number of bananas in each bunch, y, to find the total number of pieces of fruit. Hayley thinks Gretchen should add the number of apples in each bag, x, to the number of bananas in each bunch, y, and then multiply that sum by 3.
The total number of pieces of fruit that they bought should be 72.
The calculation is as follows:
Here we assume 3 bags of apples with 4 apples in each bag [tex](3 \times 4 = 12)[/tex]
And, 3 bunches of bananas with 4 bananas in each bunch [tex](3 \times 4 = 12)[/tex]
Now
= 12 + 12
= 24 pieces of fruit
Since
4 + 4 + 4 (12) apples + 4 = 4 + 4 (12) bananas
So,
= 12 + 12
= 24
here we need to multiplied by 3
So, [tex]= 24 \times 3[/tex]
= 72
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I really need help solving this problem
Answer:
108 ft2 is the area of the other rectangle
Step-by-step explanation:
If the first length is 3 and the second one is 6 if you find the width of the first rectangle, it has to be double like the length and 18*6 = 108
Answer:
108
Step-by-step explanation:
the scale is 2x
27/3 = 9
9 x 2 is 18
18 x 6 is 108
In a state lottery, 28 balls are numbered 1-28. Eight of them are randomly selected without replacement. To win, you only need to match the eight numbers drawn. Calculate the probability of winning this lottery if you purchase one ticket.
Answer:
2/7
Step-by-step explanation:
Each time you play, you get 1 number. Since 8/28 numbers win, you have a 8/28 chance to win if you buy one ticket. 8/28 = 2/7
Yoku is putting on sunscreen. He uses 2\text{ ml}2 ml2, start text, space, m, l, end text to cover 50\text{ cm}^250 cm 2 50, start text, space, c, m, end text, squared of his skin. He wants to know how many milliliters of sunscreen (c)(c)left parenthesis, c, right parenthesis he needs to cover 325\text{ cm}^2325 cm 2 325, start text, space, c, m, end text, squared of his skin. How many milliliters of sunscreen does Yoku need to cover 325 \text{ cm}^2325 cm 2 325, start text, space, c, m, end text, squared of his skin?
Answer:
13 Millilitres.
Step-by-step explanation:
Yoku uses 2ml to cover [tex]50cm^2[/tex] of his skin.
He wants to know how many millilitres of sunscreen he will need to cover [tex]325cm^2[/tex] of his body.
If Yoku covers [tex]50cm^2[/tex] of his skin will 2ml
He will cover [tex]1cm^2[/tex] of his skin with [tex]\frac{2}{50}ml[/tex] of sunscreen.
Therefore:
To cover [tex]325cm^2[/tex] of his body, he will use:
[tex]\frac{2}{50} X 325 ml\\=13ml[/tex]
he would require 13 Millilitres.
Answer:
13 is the answer!!!
Step-by-step explanation:
What is the name of segment AC in the picture? chord, radius, diameter, or circumference
Based on the circle shown above, the name of segment AC include the following: C. diameter.
In Mathematics and Euclidean Geometry, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point.
Generally speaking, the diameter of a circle simply refers to a straight line that passes through the middle (center) to the other end of the circle, thereby, measuring the distance from one end point to another.
This ultimately implies that, the diameter of a circle is double the length of the radius of a circle;
Diameter = 2 × radius
Arnold's car is 6 meters long. John's car is 500 centimeters
long. When you line them up one in front of the other, how
long are they together? (Answer in meters)
Answer:
11m.
Step-by-step explanation:
500cm=5m
6+5=11m
Simplify the following expressions using the distributive property.
6.3(m + 7) + m + 2
FOLLOW ME FOR CLEARING YOUR NEXT DOUBT
Hey there!
The Distributive Property states that
a(b+c)=ab+ac
Now simplify this expression:
6.3(m+7)+m+2
Distribute 6.3:
6.3m+44.1+m+2
Combine Like terms:
6.4m+m+44.1+2
7.4m+46.1
With this we're done!
Hope everything is clear.
Let me know if you have any questions!
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[tex]\boxed{An~Emotional~Helper}[/tex]
A rectangle on a coordinate plane has vertices Q(-1,1), R(6, 1), S(6-8), and T(-1,-8). What are the dimensions of the
rectangle?
.
The base is 6 and the height is 9.
The base is 9 and the height is 6.
The base is 7 and the height is 9.
The base is 9 and the height is 7.
Answer:
the base length of the triangle is 4 units, u can count that. and the height of triangle is 2 units, thats the dotted line one. and the equation of triangle area is (length x height) divided by 2so in this case it'll be (4x2) /2=4 square units.
Step-by-step explanation:
Answer:
The base is 7 and the height is 9
Step-by-step explanation:
vertices Q(-1,1), R(6, 1), S(6-8), and T(-1,-8)
If you look at the coordinates, you will notice that Q and R lie on line y = 1
and S and T lie on the line y = -8
so line QR || line ST
that means the height of this rectangle is |1 - -8| = 9
the length must be from point Q to R
length = |-1 - 6| = 7
dimension is 7 by 9
PLZ HELP!!!!!!! will mark brainliest!!!!
Answer:
it is many triangles
Step-by-step explanation:
Tyra has 38 counters. She now puts the 38 counters into some bags so that Each bag has an equal number. There are no counters left over. There are more than 10 counters in each bag. Work out the number of bags and number of counters in each bag.
I mean, you can divide the counters by the range 2 - 38.
I only managed to find out that 38 ÷ 2 = 19.
And 38 ÷ 19 = 2.
It says that there are more than 10 counters in each bag.
So 2 bags is the most liable option.
There are 2 bags and 19 counters in each bag.
Answer:
2 bags, 19 counters.
Step-by-step explanation:
This question is looking for factors of 38 with counters being a factor greater ten and the number of bags being the factor that multiplies the counters to get 38. First, find the factors of 38.
1 x 38 = 38
2 x 19 = 38
Since the problem says bags with an s, we can know that there has to be more than one bag. That leaves us with 2 x 19.
Q(x)=6x and r(x)=5x+1
Find (r•q)(x)
Answer:
(r * g)(x) =30xx + 6x
if it was composition
r (q(x)) = 5(6x) + 1 = 30x + 1
Step-by-step explanation:
Q(x)=6x and r(x)=5x+1
Find (r•q)(x)
multiplying the functions, right? not composition of functions.
(r * g)(x ) = (5x + 1) * 6x = 30xx + 6x
(r * g)(x) =30xx + 6x
if it was composition
r (q(x)) = 5(6x) + 1 = 30x + 1
Brian is looking at a statue in Bruso park from 8 meters away. If the distance between the top of the statue to Brian's head is 17 meters, how much taller is the statue than Brian using the Pythagorean theorem?
A cone has a slant length of 5 and a diameter of 4. What is the volume of the cone? Use π ≈ 3.14.
A.12.56 cubic units
B.18.84 cubic units
C.20.93 cubic units
D.25.12 cubic units
The volume of the cone, calculated using the given slant length and diameter, is approximately 18.84 cubic units, therefore the correct answer is B. 18.84 cubic units.
Explanation:The subject of this question is the volume of a cone. In order to calculate the volume of a cone, you need to use the formula: V = 1/3πr²h. However, in this case, you are given the slant length and the diameter. First, we need to find the radius (r) and the height (h) of the cone. The radius would be half the diameter, so r = 4/2 = 2. Then, from the given slant length (s) and radius (r), we can find the height by using Pythagoras' theorem: h = sqrt(s² - r²) = sqrt(5² - 2²) = sqrt(21). Now we can substitute r and h into the volume formula: V = 1/3*3.14*2²*sqrt(21) which is approximately 18.84 cubic units. So the answer is option B.18.84 cubic units.
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About 1/4 of all adults in the United States have type O+ blood. If three randomly selected adults donate blood, find the probability of each of the following events. (Round your answers to four decimal places.) (a) All three are type O+. 0.0156 Correct: Your answer is correct. (b) None of them is type O+. 0.4219 Correct: Your answer is correct. (c) Two out of the three are type O+.
Answer:
a) 0.0156
b) 0.4219
c) 0.1406
Step-by-step explanation:
We are given the following information:
We treat adult having type O+ blood as a success.
P(Adult have type O+ blood) = 0.25
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 3
a) All three are type O+
[tex]P(x =3)\\= \binom{3}{3}(0.25)^3(1-0.25)^0\\= 0.0156[/tex]
b) None of them is type O+
[tex]P(x =0)\\= \binom{3}{0}(0.25)^0(1-0.25)^3\\= 0.4219[/tex]
c) Two out of the three are type O
[tex]P(x =2)\\= \binom{3}{2}(0.25)^2(1-0.25)^1\\= 0.1406[/tex]
Using the principle of binomial probability, the probability o the required events are :
All three O positive = 0.0156None O positive = 0.42192 O positive = 0.1406Recall :
P(x = x) = nCx * p^x * q^(n-x) p = probability of success = 1/4 = 0.25q = 1 - p = 1 - 0.25 = 0.75n = number of trials = 3
A.) Probability that all 3 are O+ :
x = 3
P(x = 3) = 3C3 × 0.25³ × 1 = 0.0156
B.) Probability that none 3 are O+
x = 0
P(x = 3) = 3C0 × 1 × 0.75³= 0.4219
C.) Probability that 2 out of the three are O+
x = 2
P(x = 2) = 3C2 × 0.25² × 0.75¹ = 0.1406
Therefore, the required probabilities are : 0.0156, 0.4219 and 0.1406 respectively.
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on the number line which point is closest to pie
The point on a number line that is closest to Pi (π), which is approximately 3.14, would be the point representing either 3 or 4 as they are the closest whole numbers. However, a point representing 3.14 or a closer approximation would be even nearer.
Explanation:The question is asking to identify which point on a number line is closest to Pi (π), a mathematical constant that approximately equals 3.14. On a number line, you can visualize numbers as points. As Pi is 3.14 approximately, the closest point to Pi on a number line would naturally be the point that represents 3 or the point representing 4, as these are the two closest whole numbers to 3.14. However, if there's a point representing the value 3.14, or even closer approximation like 3.141, it would be even closer to Pi than the points representing 3 or 4.
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Mr. Woosley is assigning group projects to 24 students. To form the groups, each student will randomly select a slip of paper with the name of a continent on it from a bag. The student will keep the slip of paper. The number of slips of paper in the bag with each continent name is shown below. Africa - 6 Asia - 8 Australia - 4 Europe - 6 What is the probability that a student in Mr. Woosley’s class will not be assigned a project on Australia?
The probability that a student will not be assigned a project on Australia is 20/24, which simplifies to 5/6.
The probability that a student in Mr. Woosley's class will not be assigned a project on Australia can be found by subtracting the probability of being assigned Australia from 1. There are a total of 24 slips of paper representing continents, and 4 of these are Australia. Therefore, there are 24 - 4 = 20 slips that are not Australia.
The probability, P(NOT Australia), is calculated as follows
Calculate the total number of slips: 6 (Africa) + 8 (Asia) + 4 (Australia) + 6 (Europe) = 24.
Determine the number of slips that are not Australia: 24 - 4 (Australia) = 20.
Find the probability: P(NOT Australia) = Number of non-Australia slips / Total number of slips = 20 / 24.
Therefore, the probability that a student will not be assigned a project on Australia is 20/24 or 5/6 when simplified.
Find the area of the polygon:
Answer:
Step-by-step explanation:
o find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.
PLEASE HELP ME PLEASE PLEASE I NEED YOUR HELP PLEASE HELP ME Which of these expressions demonstrates the identity property? Check all that apply.
25(0) = 25
25(1) = 25
25 + 0 = 25
25 + 1 = 25
Answer:
1st one and the third one
Step-by-step explanation:
25(0)=25
25+0=25
Answer:
25(1) = 25
25 + 0 = 25
those are the correct answers
have fun goodluck and stay safe
HELP! What is the value of X? WILL GIVE BRAINLIEST!
Answer:The value of X is 7.
Step-by-step explanation: It's counting up starting at 3 so the 4..5..6..7 so, then the 6 is right one the invisible line with X
Answer:
x =2
Step-by-step explanation:
Similar triangles:-
The given triangles are same shape but not necessarily the same sizeCorresponding angles are equalCorresponding sides are in the same ratio [tex]\frac{a}{p} = \frac{b}{q} = \frac{c}{r}[/tex]Given diagram ΔABC AND ΔDBE are similar triangles.
[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]
[tex]\frac{x+x+1}{x+1} = \frac{6+4}{6}[/tex]
on simplification , we get
[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]
cross multiplication , we get
12x+6 =10x +10
12x-10x = 10 -6
2x =4
x =2
Therefore the value of x =2
verification:-
[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]
[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]
put x=2
[tex]\frac{2(2)+1}{2+1} = \frac{6+4}{6}[/tex]
[tex]\frac{5}{3} = \frac{6+4}{6}[/tex]
[tex]\frac{5}{3} = \frac{5}{3}[/tex]
both sides are equal
Therefore x value is 2
PLS HELP!! Find the value or expression for 0.
1). Sin(0) = cos (28)
2). Cos(y) = sin (0)
Answer:
1.)angle 0 = 62 degrees,
2.) angle 0 = 90 - y degrees.
Step-by-step explanation:
1). Sin(0) = cos (28)
angle 0 would be arcsin (cos (28)) = 62 degrees.
2). Cos(y) = sin (0)
angle 0 = arcsin ( cos (y) ) = 90 - y
To solve the equations involving trigonometric functions Sin(0) = cos(28) and Cos(y) = sin(0), use co-function identities to find 0 equals 62 degrees or (90° - 28°), and y could be 28 degrees or (360° - 28°) due to cosine's periodic nature.
Explanation:To solve the set of equations Sin(0) = cos (28) and Cos(y) = sin (0), we need to apply trigonometric identities and the given constraints.
Firstly, we can use the co-function identities which state that sin(90° - x) = cos(x), and similarly, cos(90° - x) = sin(x). Therefore, for the first equation, we can express 0 in terms of 28°:
sin(0) = cos(28°) implies 0 = 90° - 28° or 0 = 62°.
For the second equation, we replace 0 with 62°:
cos(y) = sin(62°)
We know that sin(62°) equates to the same value as cos(28°) from the first equation.
Therefore, cos(y) = cos(28°), which means y = 28° or y = 360° - 28° due to the periodic nature of cosine.
3
Circle the shapes that are congruent.
Answer:
Shapes 1 and 3 are congruent
Step-by-step explanation:
The only thing different between them is that the first one is tilted to look different.
Answer:
the 1st and 3rd one.
Step-by-step explanation:
the first 3 are similar in shape but, the 1st and 3rd one are congruent because they have the same size and shape.
25 pts! Math question!!!
Answer:
6051
Step-by-step explanation:
fo sho
Solve the quadratic by factoring.
x^2-5x-31=5
Final answer:
The quadratic equation x²-5x-31=5 is solved by factoring to (x - 9)(x + 4) = 0, giving the solutions x = 9 and x = -4.
Explanation:
To solve the quadratic equation x²-5x-31=5 by factoring, we first move all terms to one side to get it into standard form:
x² - 5x - 36 = 0
Next, we look for two numbers that multiply to -36 and add up to -5. These numbers are -9 and 4. So, we can write:
(x - 9)(x + 4) = 0
Now, we have two possible solutions for x:
x - 9 = 0, which gives us x = 9x + 4 = 0, which gives us x = -4Therefore, the solutions to the equation are x = 9 and x = -4.