Which value for x makes the sentence true?
4/5x = 5/6
A.
25/24
B.
2/3
C.
49/30
D.
1/30
C. 49/30
Roger built a model car of a station wagon he actually owns. Based on the ratio on the box, he knows that every inch in the length of his model car represents 25 inches of length in his actual station wagon. The station wagon's car manual shows that the length of the actual car is 193.75 inches.
Complete the following equation so that it can be used to find the length, m, of the model car, then find the length of the model car.
The length of the model car is
inches.
The equation is:
m/1 = 193.75/25
Simplifying, we get:
m = 7.75
Therefore, the length of the model car is 7.75 inches.
Roger built a model car of a station wagon he actually owns. Based on the ratio on the box, he knows that every inch in the length of his model car represents 25 inches of length in his actual station wagon. The station wagon's car manual shows that the length of the actual car is 193.75 inches.
Complete the following equation so that it can be used to find the length, m, of the model car, then find the length of the model car.
The equation is:
m/1 = 1/25 * 193.75
Simplifying, we get:
m = 7.75 inches
Therefore, the length of the model car is 7.75 inches.
Wanda has two times more shirts than her brother, Will.
The equation a = 2b, where a represents the number of shirts Wanda has, and b represents the number of shirts Will has, shows this relationship.
If Wanda has 18 shirts, how many shirts does Will have?
From the given equation, we know that a = 2b. We also know that a = 18, since Wanda has 18 shirts.
Substituting a = 18 into the equation, we get:
18 = 2b
To solve for b, we can divide both sides by 2:
b = 9
Therefore, Will has 9 shirts.
508 + x = 731
To solve for x, we need to isolate it on one side of the equation.
We can do this by subtracting 508 from both sides:
508 + x - 508 = 731 - 508
Simplifying, we get:
x = 223
Therefore, x equals 223.
Leo and Lucy are making friendship bracelets. Leo has two times more beads than Lucy.
The equation given below shows this relationship, where p represents the number of beads Leo has, and q represents the number of beads Lucy has.
If Leo has 12 beads, how many beads does Lucy have?
From the given equation, we know that p = 2q. We also know that p = 12, since Leo has 12 beads.
Substituting p = 12 into the equation, we get:
12 = 2q
To solve for q, we can divide both sides by 2:
q = 6
Therefore, Lucy has 6 beads.
Rick and Jim are working at the concession stand at the school basketball game. Rick sells 18 more burgers than Jim.
The equation given below shows this relationship, where g represents the number of burgers Rick sells, and h represents the number of burgers Jim sells.
If Rick sells 38 burgers, how many burgers does Jim sell?
From the given equation, we know that g = h + 18. We also know that g = 38, since Rick sells 38 burgers.
Substituting g = 38 into the equation, we get:
38 = h + 18
To solve for h, we can subtract 18 from both sides:
h = 20
Therefore, Jim sells 20 burgers.
Valorie made four times more baskets than her brother, Vance.
The equation v = 4n, where v represents the number of baskets Valorie made, and n represents the number of baskets Vance made, shows this relationship.
If Valorie made 52 baskets, how many baskets did Vance make?
From the given equation, we know that v = 4n. We also know that v = 52, since Valorie made 52 baskets.
Substituting v = 52 into the equation, we get:
52 = 4n
To solve for n, we can divide both sides by 4:
n = 13
Therefore, Vance made 13 baskets.
6,278 + x = 6,986
To solve for x, we need to isolate it on one side of the equation.
We can do this by subtracting 6,278 from both sides:
6,278 + x - 6,278 = 6,986 - 6,278
Simplifying, we get:
x = 708
Therefore, x equals 708.
0.14x = 0.3612
To solve for x, we need to isolate it on one side of the equation.
We can do this by dividing both sides by 0.14:
0.14x/0.14 = 0.3612/0.14
Simplifying, we get:
x = 2.58
Therefore, x equals 2.58.
Jerry and Stella are working on an art project together. Jerry has 12 more markers than Stella.
The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has.
If Jerry has 45 markers, how many markers does Stella have?
From the given equation, we know that u = t + 12. We also know that u = 45, since Jerry has 45 markers.
Substituting u = 45 into the equation, we get:
45 = t + 12
To solve for t, we can subtract 12 from both sides:
t = 33
Therefore, Stella has 33 markers.
Beth and Amy are trading marbles. Beth has two times more marbles than her sister, Amy.
The equation given below shows this relationship, where x represents the number of marbles Beth has, and y represents the number of marbles Amy has.
If Beth has 12 marbles, how many marbles does Amy have?
From the given equation, we know that x = 2y. We also know that x = 12, since Beth has 12 marbles.
Substituting x = 12 into the equation, we get:
12 = 2y
To solve for y, we can divide both sides by 2:
y = 6
Therefore, Amy has 6 marbles.
If x = 3 units, y = 6 units, and h = 5 units, find the area of the parallelogram shown above using decomposition.
Bot help me
Of course! We'll use the formula for the area of a parallelogram, which is:
area = base x height
In this case, we have two possible bases: x and y. We can choose either one, because the area of a parallelogram does not depend on which side we choose as the base.
Let's use y as the base. Then the height will be x, because the height of a parallelogram is always perpendicular to its base.
The area of the parallelogram can be decomposed into a rectangle and two triangles, as shown below:
```
y
┌────────────┐
x │ │
│ ▲ ▲ │
│ / \ │
│ / \ │
│/_______\___│
```
The rectangle has height x and length h, so its area is:
A = xh
Each triangle has base x and height (y - x), so each triangle's area is:
A = (1/2) * x * (y - x)
To find the total area of the parallelogram, we can add the area of the rectangle and the area of the two triangles:
A = xh + 2 * (1/2) * x * (y - x)
Simplifying, we get:
A = xh + x(y - x)
Now we can substitute the given values:
A = 3 * 5 + 3 * (6 - 3)
A = 15 + 9
A = 24
Therefore, the area of the parallelogram is 24 square units.
Do a different method please bot
Sure! Another way to find the area of the parallelogram is by drawing a diagonal, which divides the parallelogram into two congruent triangles. The diagonal has length z, which we can find using the Pythagorean theorem.
```
y
┌────────────┐
x │ │
│ / │
│ / │
│ / │
│/___________│
```
In this picture, we have a right triangle with legs x and h, and hypotenuse z:
```
z
┌─────┐
│ │
x │ │h
│ │
└─────┘
```
Using the Pythagorean theorem, we can solve for z:
z^2 = x^2 + h^2
z^2 = 3^2 + 5^2
z^2 = 34
z = sqrt(34)
Now, the area of each triangle is (1/2) * x * h, so the total area of the parallelogram is:
A = 2 * (1/2) * x * h
A = x * h
Substituting the given values, we get:
A = 3 * 5
A = 15
Therefore, the area of the parallelogram is 15 square units.
If x = 4 units, y = 4 units, and h = 7 units, find the area of the trapezoid shown above using decomposition.
We'll use the formula for the area of a trapezoid, which is:
area = (base1 + base2) x height / 2
In this case, we have two possible bases: x and y. We can choose either one, because the area of a trapezoid does not depend on which side we choose as the bases.
Let's use y as the top base and x as the bottom base:
```
y y
┌────────────┐
│ │
│ │
x │ │ x
│ │
└────────────┘
y
```
The height of the trapezoid is h. We can decompose the trapezoid into two triangles and a rectangle, as shown below:
```
y y
┌────────────┐ ┌────────────┐
│ ▲ │ │ │
│ | h │ │ │
x │ | │ x │ │ x
│ ▼ │ │ │
└────────────┘ └────────────┘
y y
```
The rectangle has length y and height h, so its area is:
A_rect = yh
Each triangle has base (y - x)/2 and height h, so each triangle's area is:
A_tri = (1/2) * (y - x)/2 * h
To find the total area of the trapezoid, we can add the area of the rectangle and the area of the two triangles:
A = yh + 2 * (1/2) * (y - x)/2 * h
Simplifying, we get:
A = yh + (y - x)/2 * h
Now we can substitute the given values:
A = 4 * 7 + (4 - 4)/2 * 7
A = 28
Therefore, the area of the trapezoid is 28 square units.