Given a rectangle with sides in a 3:4 ratio and a perimeter of 42 cm, the length of the shortest side is 9 cm.
Explanation:We are given that the sides of the rectangle are in a 3:4 ratio and that the perimeter is 42 cm. The rectangular perimeter is calculated by the formula 2*(length + width). In this case, because the sides are in a 3:4 ratio, we can say 2*(3x + 4x) = 42, where 'x' represents the length of the shortest side.
Solve this equation, 2*(7x) = 42, we find that 'x' is 3. So the length of the shorter side, 3x, is 9 cm. Applying the same 3:4 ratio, the longer side, 4x, is 12 cm.
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To find the length of the shorter side of a rectangle with sides in a 3:4 ratio and a perimeter of 42cm, we set up an equation using the ratio values as coefficients and the known perimeter. Solving this equation shows that a unit in the ratio equals 3cm and the shorter side is 9cm.
Explanation:In this mathematics problem, we are trying to find the length of the shorter side of a rectangle, knowing that the sides are in a 3:4 ratio and that the perimeter is 42cm. The perimeter of a rectangle can be found by using the equation [tex]P=2L+2W[/tex] (Perimeter equals twice the length plus twice the width).
If we represent the shorter side as 3x and longer side as 4x, we can establish the following equation based on the given perimeter:[tex]2*(3x)+2*(4x)=42c[/tex]m. Simplifying this equation gives 14x=42cm. Solving for 'x', we find x=3. Therefore, each unit in the ratio corresponds to 3cm, and the length of the shorter side, represented by 3x, is [tex]3*3=9[/tex]cm.
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a vertical pole 10 meters high, casts a shadow 8 meters long. at the same time, a nearby tree casts a shadow 40 meters long. find the height of the tree in meters
You and your friend Sam are going to paint your 300 square feet room together.
Sam takes 10 minutes to paint 25 square feet.
You take 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take us 15 minutes to paint 50 square feet!''
Write a EXCEPTIONAL explanation to convince Sam that he is wrong. Thank You.
A pizza shop offers 12 different topping choices. if you order a large pizza with two toppings, how many possibilities would you have?
What percent of data set is represented in Q1
Use Euler’s Formula to find the number of edges in a polyhedron with seven faces: two pentagons and five rectangles.
To determine the number of edges in a polyhedron with seven faces, two being pentagons and five being rectangles, you apply Euler's formula, resulting in a total of 15 edges.
To find the number of edges in a polyhedron with seven faces using Euler's formula, which is V - E + F = 2, we first need to determine the number of vertices (V) and faces (F) of the polyhedron.
Given that the polyhedron has two pentagons and five rectangles, we can calculate the total number of vertices. Each pentagon has 5 vertices and each rectangle has 4, but since rectangles share sides, some vertices will be counted twice.
Therefore, for the rectangles, we should calculate the vertices as if there were four distinct ones and then subtract the overlaps. Assuming all rectangles share exactly one side with its adjacent, we would have 4 vertices for each rectangle minus 2 for each shared side, resulting in 2 vertices per rectangle.
With five rectangles, that's 10 vertices, plus the 10 from the two pentagons, we get 20 vertices in total. Now, we apply Euler's formula: V - E + F = 2, substituting the values:
E = V - F + 2
E = 20 - 7 + 2
E = 15
Therefore, the polyhedron has 15 edges. .
Which solid has a volume that is 3 times the volume of a cone with the same base and height?
a.cylinder
b.prism
c.pyramid eliminate
d.sphere?
Ok My last 2 questions please!!!
PLEASE HELP!
The center of a circle is at (2, −5) and its radius is 12.
What is the equation of the circle?
(x−2)2+(y+5)2=144
(x+2)2+(y−5)2=144
(x+2)2+(y−5)2=24
(x−2)2+(y+5)2=24
hELPP
A total of 300 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adults tickets sold. How many adult tickets were sold?
By setting up and solving an equation, it was determined that 75 adult tickets were sold for the school play.
To solve the problem of determining how many adult tickets were sold for the school play, we can set up an equation. Let's represent the number of adult tickets sold as A, and since the number of student tickets sold was three times that of adult tickets, we can express the student tickets sold as 3A. We know the total tickets sold were 300, so the equation to represent this scenario is:
A + 3A = 300
Combining like terms, we get:
4A = 300
Dividing both sides of the equation by 4 to solve for A gives us:
A = 300 / 4
A = 75
Therefore, 75 adult tickets were sold.
What is compound interest?
A - the interest earned on the principal of an investment
B - the interest earned on both the principal and interest of an investment or savings account
C - the interest earned on a mutual fund
D - the interest earned on a loan
The correct answer is
The interest is earned on the principal and interest earned previously
:)
A technician is launching fireworks near the event of a show. Of the remaining 11 fireworks, 4 are blue and 7 are red. If she launches 6 of them what’s the probability that 2 of them will be blue
[tex] \displaystyle
|\Omega|=\binom{11}{6}=\dfrac{11!}{6!5!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\
|A|=\binom{4}{2}=\dfrac{4!}{2!2!}=\dfrac{3\cdot4}{2}=6\\\\
P(A)=\dfrac{6}{462}=\dfrac{1}{77}\approx1\% [/tex]
PLS HELP ME ASAP WITH THESE! THANKS!!
(Brainliest will be given hopefully)
(Random answers gets moderated.)
What happens to correlation if you multiply every x in the data set by .5?
Find the possible values of the included angle of a triangle with: A) sides of length 5 cm and 8 cm, and area of 15 cm^2
B) sides of length 45 km and 53 km, and area 800 km^2.
Jesse made a model of a mountain range for class. to do this, he bought a cylinder of cardboard and cut it into three cones. each cone is 5 inches tall and has a diameter of 4 inches. what was the volume of the original cylinder jesse bought in terms of \piπ?
The volume of the original cylinder that Jesse bought is 20π cubic inches.
To find the volume of the original cylinder Jesse bought, we need to use the volume formula for a cylinder:
V = πr²h
First, we need to find the volume of each cone using the formula:
Volume of a cone = (1/3)πr²h
Given:
Height(h) of each cone = 5 inchesDiameter of each cone = 4 inches, so the radius(r) = 4/2 = 2 inchesVolume of one cone:
V_cone = (1/3)π(2)²(5) = (1/3)π(4)(5) = (20/3)π cubic inches
Total volume of three cones:
V_total_cones = 3 × (20/3)π = 20π cubic inches
Since the volume of the cylinder equals the total volume of the cones:
V_cylinder = 20π cubic inches
Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.
Sample Response: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.
(on the assignment)
The probability that the Cubs win their first game is 1/3. The probability that the Cubs win their second game is 3/7. What is the probability that the Cubs win games?
The correct answer is:
1/7.
Explanation:
The two events, the Cubs winning their first game and the Cubs winning their second game, are independent. This is because the Cubs winning their first game does not affect the probability of the Cubs winning their second game.
Since the events are independent, to find the probability that both events occur, multiply the probabilities:
1/3(3/7) = (1*3)/(3*7) = 3/21 = 1/7
An organization will give a prize to a local artist. The artist will be randomly chosen from among 10 painters, 3 sculptors, and 5 photographers. What is the probability that the artist chosen will be a sculptor or a photographer?
The probability is 8/18 or 44%.
Since there are 3 sculptors and 5 photographers, and the question is asking for either a sculptor or photographer, you add them together. There are a total of 18 artists, and the probability is the chance of a certain thing happening over the total amount of things that can happen (i.e. a coin landing on heads is 50%).
The answer would be 8/18.
The area of the sector formed by the 110 degree central angle is 40 units squared what is the radius
What is y+7/7y÷3y^2+21y/14y−5 simplified?
If the exchange rate changes from $1.45 = 1 euro to $1.37 = 1 euro, then
Prove that x²+6x+18 is always greater than
[tex]2 - \frac{1}{x} [/tex]
For any value of x.
On Monday, there was no snow on the ground in Buffalo, New York. On Tuesday, three inches of snow fell.On Wensday a half an inch of snow melted. On Thursday two and a half more inches fell. On Friday another inch and a half melted. How much snow was left on the ground Friday night.
write an inequality for the following situation
No more than 8 books are in your bag
A. x ≤ 8 B. x < 8 C. x ≥ 8 D. x > 8
100 points! Evaluate the equation. Look at the picture. Do #7.
The ratio of men to women working for a company is 4 to 5. if there are 52 men working for the company, what is the total number of employees?
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman. Another flower is then chosen at random and given to a different woman. What is the probability that both flowers are pink roses?
In which quadrant of the coordinate plane is (-2a - 3, -3b - 5), if a = -3 and b = 3?
After substituting a = -3 and b = 3 into the point (-2a - 3, -3b - 5), we get the point (3, -14), which lies in the fourth quadrant of the coordinate plane.
To determine in which quadrant of the coordinate plane the point (-2a - 3, -3b - 5) is located, we substitute the values a = -3 and b = 3 into the coordinates. First, for the x-coordinate we have:
-2(-3) - 3 = 6 - 3 = 3
And for the y-coordinate:
-3(3) - 5 = -9 - 5 = -14
The resulting point is (3, -14), which is located in the fourth quadrant because the x-value is positive and the y-value is negative.
Write the first 6 terms of an arithmetc sequence if the first number is 9 and the common diffrence is 5
1. What is the value of x in the equation –6 + x = –2?
A. 4
B. –8
C. 8
D. –4
2.
How many solutions does the equation –3a + 3a + 6 = 7 have?
A. Infinitely many
B. Two
C. One
D. None
3.
What is the solution to the equation 1.2m – 0.8 = –2.0m?
A. m = 0.25
B. m = 4
C. m = 1
D. m = 0.4
4.
How many solutions does the equation 4p + 7 = 3 + 4 + 4p have?
A. Two
B. Infinitely many
C. None
D. One
5.
What is the value of y in the equation 2(2y – 12) = 0?
A. 4
B. 8
C. 7
D. 6
6.
What is the value of z in the equation 2(4z – 9 – 7) = 166 – 46?
A. 19
B. 34
C. 26
D. 21
7.
Which of these is a simplified form of the equation 7y + 7 = 9 + 2y + 2y?