The solution set of the equation is Ø.
A triangular prism has a cross-sectional area of 15 cm squared and a volume of 225 cm squared.
What is the length of the prism?
The length of the triangular prism that has a volume of 225 cm³ and cross-sectional area of 15 cm² is calculated as: 15 cm.
What is the Volume of a Triangular Prism?A triangular prism looks like the shape shown in the image that is attached below. The shaded part is the cross-sectional area of the triangular prism.
The volume of a triangular prism = area of cross-section × length of the prism
The volume of a triangular prism = (1/2 × b × h) × l
Given the following:
Cross-sectional area of the triangular prism = 15 cm²
Length of the triangular prism = l
Volume of the triangular prism = 225 cm³
Substitute the values into the given formula for the volume of the prism:
225 = 15 × l
225 = 15l
Divide both sides by 15
225/15 = 15l/15
15 = l
l = 15 cm
Length of the prism is therefore 15 cm.
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The cost of 5 kg of oranges is sane as the cost of 3 kg of apples. How many kilograms of oranges are required to exchange 9 kg of apples ?
Answer:
7kg
Step-by-step explanation:
What is value of x in the equation below? 33 ≥ -6x + 9
Answer:
x ≥ -4
or [-4, ∞)
Step-by-step explanation:
What is value of x in the equation below?
33 ≥ -6x + 9
subtract 9 from both sides:
33 - 9 ≥ -6x + 9 - 9
24 ≥ -6x
divide both sides by -6 and remember to flip sign direction:
24/-6 ≥ -6x/-6
-4 ≤ x
or: x ≥ -4
in set builder notation: [-4, ∞)
Answer:
Below in bold
Step-by-step explanation:
33 ≥ -6x + 9
-6x ≤ 33 - 9
-6x ≤ 24
x ≥ -4
- note that the inequality is flipped as we are dividing by a negative.
what is -15 divided (-3) ?
Answer:
its positive 5 a negative divided by a negative is a positive
Step-by-step explanation:
Answer:
Positive 5
Step-by-step explanation:
a negative divided by a negative or a negative multiplied by a negative will always equal a positive. This equation is equal to 15 divided by 3 which is equal to 5.
a girl is standing at one corner of a snowy rectangular field that measures 100 ft by 100 ft, as drawn. she wishes to reach a warm cabin located at the diagonally-opposite corner of the field. suppose she trudges through the snow at 3 ft/sec to reach a point p at the other side of the field, then walks the remaining distance along a plowed road at 5 ft/sec to reach the cabin. in order to reach the cabin as quickly as possible, how far is point p from the cabin?
For Sally to reach the cabin fastest the distance from point P to the distance cabin at point C must be 25 ft
Let Sally be at point S and the cabin diagonal-opposite to her at point C. We need to find the distance between P and C such that Sally reaches the cabin the quickest. We know SX = 100ft
By Pythagoras' theorem
SX² + XP² = SP²
⇒100² + x² = SP²
⇒SP = √(100²+x²) (1)
speed = distance/ time
⇒ time = distance / speed
We need to minimize the time taken by sally
time taken to reach cabin t = (SP/3) + (PC/5)
⇒t = (SP/3) +(PC/5)
⇒t = (√(100²+x²) /3) + (PC/5)
⇒t = (√(100²+x²) /3) + (100-x/5)
⇒dt/dx = x/ (3*√(100²+x²)) -(1/5) = 0 (to minimize)
⇒5x = 3√(100²+x²)
⇒25x² = 9(100² + x²)
⇒16x² = 90000
⇒x²= 5625
⇒x = √5625
⇒x= 75 ft
Thus the distance from point P to cabin C = PC = 100 - x = 100-75=25 ft
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(2x+3)(4x-7) , you get a new expression of the form ax^2+bx+c what is value of a , b , and c
(2x+3)(4x-7)
To convert this quadratic formula on the general expression, we need to multiply both parenthesis as follows:
8x^2 - 14x + 12x - 21 =
8x^2 -2x - 21
where a, b and c correspond to the coefficients of the equation:
a = 8
b = -2
c = -21
Each baby dinosaur made 151515 paintings and each adult dinosaur made 777 paintings. The entire herd made 208208208 paintings in total, and there were 333 times as many baby dinosaurs as adult dinosaurs.
How many baby dinosaurs and adult dinosaurs were there?
Using the expression, 15x + 7y = 208 there were x = 12 baby dinosaurs and y = 4 adult dinosaurs.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Each baby dinosaur made 15 paintings and every adult dinosaur made 7 paintings.
The total number of paintings the entire herd made is 208.
There were 3 times as many baby dinosaurs as adult dinosaurs.
Now, let x be the number of baby dinosaurs and y be the number of adult dinosaurs.
Then,
x = 3y
So,
The expression for the total number of paintings will be:
208 = 15x + 7y
208 = 15(3y) + 7y
208 = 45y + 7y
208 = 52y
y = 4
So,
x = 3y = 3(4) = 12
There were 12 baby dinosaurs and 4 adult dinosaurs.
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Find the number that makes the ratio equivalent to 1:9.Find the number that makes the ratio equivalent to 1:9. 4:
The number that makes the ratio equivalent to 1:9 include 2 and 18.
The numbers that number that makes the ratio equivalent to 1: 9: 4 include 2, 18, and 8.
How to illustrate the information?It should be noted that ratio is used to show the comparison between the numbers illustrated.
It should be noted that based on the information, 1:9 is equivalent to 2 and 18. This can be illustrated as:
= 2/18 = 1/9.
Also, 1:9:4 equals 2, 18 and 8. In their case, the ratio is multiplied by 2 to get the numbers.
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What is the LCD of 11/7 and 3/8?
Using the LCD of 2 fractions formula, it was determined that the LCD of 11/7 and 3/8 is 33.
What does LCD mean in mathematics?When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.
LCD of 11/7 and 3/8 is given as follows:
We know that,
LCD of 2 fractions = (LCD of a,b)/(HCF of a,b) where a and b are two fractions.
LCD = (LCD of 11/7 and 3/8)/(HCF of 11/7 and 3/8)
= 33/1
Therefore, the LCD of 11/7 and 3/8 is found to be 33 which was calculated using the formula of LCD of 2 fractions.
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What is y equal to ?
y=10, hope that helps.
PLEASE HELP: answer following questions, will make brainliest!
For each question give the output of each expression with the given input.
A.
F(x) =x +3
F(4)=
B.
F(x)=2x-9
F(5)=
C.
F(x)= -6x+2
F(-3)=
I got -3(23q+15) but it says its wrong
Answer:
-72q - 48
Step-by-step explanation:
Use didtributive property to multiply -9 by 5 + 9q-3 - 45 - 72qSubtract 45 from -3 to get -48-48 - 72qThe you have to switch the equation around to because the variable has to be on the left.Answer:
-75q - 45
Step-by-step explanation:
Given expression,
→ -3q - 9(5 + 8q)
Simplifying the expression,
→ -3q - 9(5 + 8q)
→ -3q + (-9 × 5) + (-9 × 8q)
→ -3q - 45 - 72q
→ -75q - 45
Hence, answer is -75q - 45.
A sea Lion is at sea level it dove at a rate of 7.3 feet per minute. what is the elevation of the sea lion after half an hour?
unit rate for 3ounces cost $2.73
The unit rate for 3 ounces cost $2.73 is 0.91 dollars per ounces.
How to find unit rate?Unit rate is the ratio of two different units, with denominator as 1.
In other words, a unit rate is a rate where the second quantity is one unit , such as $28 per pound, 30 metres per hour, 15 Nigerian naira per Brazilian Real, etc.
Therefore, let's find the unit rate for 3 ounces cost $2.73.
Hence,
unit rate = cost / amount in weight
cost = $2.73
amount in weight = 3 ounces
Therefore,
unit rate = 2.73 / 3
unit rate = 0.91 dollars per ounces
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calcular la altura del sol sobre el horizonte (medida en ángulo) si un edificio de 24 metros de altura proyecta una sobra de 30 metro
Usando propiedades de triangulos rectangulos veremos que el angulo de elevación es 38.65°
¿Como encontrar el angulo de elevacion del sol?
El ángulo de elevación del sol sera el angulo que esta en el vertice derecho del triangulo rectangulo en la imagen.
Sabemos que:
tan(a) = (cateto opuesto)/(cateto adjacente).
En este caso:
cateto opuesto = 24m
cateto adjacente = 30m
Entonces:
tan(a) = 24m/30m = 0.8
Aplicando la funcion inversa, obtenemos:
a = Atan(0.8) = 38.65°
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if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s.
a. True
b. False
The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.
What is the linearly dependent set?A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.
If S is a linearly dependent set, then each vector in S is a linear combination of the others.
This is false.
For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.
If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.
Hence, the correct answer would be option (B).
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find the quotient of 4296 and 4
Answer: 1074
Step-by-step explanation:
Since quotient means division, the question would be 4296 divided by 4. So the answer would be 1074.
A mountain climbing team meets at a basecamp and drives up to a trailhead to start their climb. The trailhead is at 0 feet above sea level. For each of the first three
days, they climb 250 feet vertically. The fourth day, they climb another 150 feet vertically to the summit of the mountain. Over the final three days, the climbers
descend the mountain, decreasing their altitude by 325 feet each day until they get back to the basecamp where they first met.
Select options below
1. During their climb, the climbers increase their altitude by Select Option
vertical feet.
2. After they summit the mountain, they decrease their altitude by Select Option vertical feet.
3. This means the basecamp where they first met is Select Option
Answer:
1. 900
2. 975
3. 75 feet below sea level? which makes no sense but that's what the math says.
solve each compound inequality and graph the solution!!! I need answers and step by step equations for 20,22, and 24 please!!!!!!
The answer for 20 is ( ∞ , 4) .
The answer for 22 is ( ∞ , 3) .
The answer for 24 is ( -∞ , -24/11) .
What is compound inequality?An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."(20) 2x - 5 > 3
x > 8/2
x > 4
Hence , ( ∞ , 4)
(22) -x + 1 > -2
x > 3
Hence , ( ∞ , 3)
(20) -5/8x + 2 + 3/4x > -1
11x > -24
x > -24/11
Hence , ( ∞ , -24/11)
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georgie works 15 hours each week
she earns 5 pound per hour
georgie saves 1/3 of hr earnings each week
how many weeks does it take georgie to save 200 pound
HELP ASAP
A 2-column table with 5 rows titled Nutritional Facts Strawberries (1 ounce). Column 1 has entries calories, fat, carbohydrates, fiber, protein. Column 2 has entries 6.1, 0.1 gram, 1.25 grams, 0.41 grams, 0.2 grams. Marisol’s spinach salad calls for 3.2 ounces of sliced strawberries. How many grams of fiber are in the strawberries she is using? The strawberries contain grams of fiber.
Applying the ratio of 1-ounce strawberries to 3.2-ounces strawberries, the grams of fiber Marisol uses in the strawberries is 1.312 grams.
What is the ratio?The ratio is the numerical relationship that two values share.
Ratios show proportional values to explain how much one variable is contained in another.
Ratios are represented using the ratio sign (:) or using percentages, decimals, or fractions.
Nutritional Facts
Strawberries (1 ounce)
Calories 6.1 grams
Fat 0.1 gram
Carbohydrates 1.25 grams
Fiber 0.41 grams
Protein 0.2 grams
Fiber = 1.312 grams (0.41 x 3.2)
Thus, Marisol needs 1.312 grams of fiber, given the ratio requirements.
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(4, -3); 2x - 7y = 12
what the perpendicular given line?
The slope that is perpendicular to the line (2x - 7y = 12) is -7/2.
What is the slope?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points lying on a straight line, a slope can be calculated using a variety of methods.So, let's represents the given equation (2x - 7y = 12) in the slope-intercept form y = mx + b:
Add -2x on both sides as follows:
-7y = -2x - 12Divide everything by -7 as shown:
y = 2/7x + 12/7The slope of the line is 2/7.The perpendicular line's slope is equal to the given line's negative reciprocal: -7/2
Therefore, the slope that is perpendicular to the line (2x - 7y = 12) is -7/2.
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The correct question is given below:
How do you find the slope that is perpendicular to the line 2x - 7y = 12?
Samson uses 6 gallons of water on 20 plants in his garden.
At that rate, how much water will it take to water 30 plants
A line passes through the point (-3, -2) and has a slope of
1.
What is the equation of the line?
y=x+1
y=-x-1
3
y=-x-1
4|3
Answer:
y=x+1
Step-by-step explanation:
first use the equation in point - slope form:
y+2=1(x+3)
then rearrange them to make it in slope intercept form - y=mx+b
y= 1x + 1 or y=x+1
Find the value of x, y, and z. (see picture)
z=72°+57°(EXTERIOR ANGLES OF A TRIANGLE)
z=129°
x+57°=180°(ANGLES ON A STRAIGHT LINE)
x=180°-57°
x=123°
y+72°=180°(ANGLES ON A STRAIGHT LINE)
y=180°-72°
y=108°
HOPE THIS HELPS.
I need help please this is going in my grade book:((
Josie has more race to complete.
Define fraction.The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is [tex]\frac{1}{2}[/tex].
Given Data
Josie has completed [tex]\frac{8}{25}[/tex]
Caroline has completed 40%
Converting percentage into fraction,
[tex]\frac{34}{100}[/tex]
Simplifying,
[tex]\frac{17}{50}[/tex]
For comparing, we need to have same denominators.
So,
[tex]\frac{8}{25}[/tex] ×[tex]\frac{2}{2}[/tex]
[tex]\frac{16}{50}[/tex]
[tex]\frac{17}{50}[/tex] > [tex]\frac{16}{50}[/tex]
Josie has more race to complete.
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A small cube has sides that are 1/2 cm. How many small cubes would fit
inside a rectangular prism that has a length of 10, a width of 5, and a height
of 2?
min
2 cm
5 cm
in
10 cm
67 cubes of area 1.5 cm² can be fitted in the rectangular prism of volume 100 cm³.
What exactly is a rectangular prism?A rectangular prism can also be referred to as a "cuboid."Though it appears to be a cube, it is not.The only difference between it and a cube is that it has rectangle-shaped faces as opposed to a cube's square faces.A cuboid is a six-sided solid in geometry known as a hexahedron.Its faces are quadrilaterals.In the sense that a cuboid can be transformed into a cube by changing the length of its edges or the angles between its faces, the word "cuboid" means "like a cube."So, first, we need to find the volume of the rectangular prism as follows:
The formula for the volume of the rectangular prism: V= whl
Substitute values as follows:
V = whlV = 5 × 2 × 10V = 100The volume of a rectangular prism is 100 cm³.
Now, the area of the cube:
The formula for the area of the cube: is 6a²
The area of the cube is 1.5 cm².
A number of cubes that can be fitted in the rectangular prism:
100/1.5 = 66.667Rounding off: 67Therefore, 67 cubes of area 1.5 cm² can be fitted in the rectangular prism of volume 100 cm³.
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The correct question is given below:
A small cube has sides that are 1/2 cm. How many small cubes would fit inside a rectangular prism that has a length of 10, a width of 5, and a height of 2?
Make is filling grocery bags at a foot pantry. Each bag's contents will be identical, and there will be no food left over. Mike has 27 boxes of oatmeal and 18 boxes of raisins.
3. what is the greatest number of bags can she fill?
4. how many boxes of each food will go in each bag?
__ boxes of oatmeal __ boxes of raisins
please help asap thank u so much
The greatest number of bags that she can fill is 9.
The number of boxes of oatmeal that will be in each bag is 3
The number of boxes of raisins that will be in each bag is 2
What is the greatest number of bags she can fill?In order to determine the greatest number of bags that she can fill, we needed to determine the highest common factor of 18 and 27. The highest common factor of a number is the greatest number that perfectly divides two or more numbers.
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 27 = 1, 3, 9, 27
Highest common factor = 9
The greatest number of bags that she can fill is 9.
Number of boxes of oatmeal that will be in each bag: 27 / 9 = 3
Number of boxes of raisins that will be in each bag: 18 / 9 = 2
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Find the length of side BC.
Give your answer to 3 significant figures.
C
A
71°
6.3 cm
B
From the given diagram, the size of side BC is 19.4 rounded to 3 significant figures
What is trigonometric function?The trigonometric functions are real functions that relate the angle of a right-angled triangle to side length ratios. They are widely used in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many others.The values of all trigonometric functions based on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.From the given diagram, the size of side BC is 19.4 rounded to 3 significant figures
Given
The right angle triangle with a side and an angle
We must find out the hypotenuse BC
We are given with adjacent side AB
Let's use trigonometric ratio
[tex]$&\cos (B)=\frac{\text { adjacent }}{\text { hypotenuse }} \\[/tex]
[tex]$&\cos (71)=\frac{A B}{B C} \\[/tex]
[tex]$&\cos (71)=\frac{6.3}{B C} \\[/tex]
[tex]$&B C \cos (71)=6.3 \\[/tex]
[tex]$&B C=\frac{6.3}{\cos (71)}[/tex]
Use the calculator to find out BC
BC=19.3508
Round the answer to 3 significant figures
So BC= 19.4
Length of side BC = 19.4
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Triangle A has a single transformation performed on it to create Triangle B. Michelle says the single transformation must have been a translation 8 units to the right.
what is the transformation that could have been performed on Triangle A to create Triangle B to prove Michelle's statement is false.
Answer:The single transformation that maps triangle A onto triangle B is the reflection about the x-axis
Step-by-step explanation:
