Step-by-step explanation:
Let's use this equation as an example - [tex]102=-7r+4[/tex]
The whole point of a linear equation is to find what the variable (which in our case is r ) equals to.
Our equation: [tex]102=-7r+4[/tex]
First step is to try to get r alone on one side.
First step: [tex]102-4=-7r[/tex] we wouldn't do [tex]102+4=-7r[/tex] (notice it's negative and not positive) since we're switching the positive 4 to the other side we'd switch the positive to a negative, making it [tex]102-4[/tex].
Know that everytime we switch a number or variable to the other side we must always switch the sign to the opposite of what it is. If it's dividing, we multiply, if we subtract, we add, etc. Same with the other way around.
Second step is to solve both sides of the equation.
Second step: [tex]98=-7r[/tex]
Third step is to divide the both sides by the number with the variable, making it 98 divided by -7r and -7r divided by -7
Third Step: [tex]\frac{98}{-7} =\frac{-7r}{-7}[/tex] = [tex]-14=r[/tex]
Now we've found our variable.
Answer: [tex]-14=r[/tex]
What is the surface area of a triangular prism with dimensions of 10m, 9m, 6m, and 8m?
The surface area of the triangular prism with dimensions of 10m, 9m, 6m, and 8m is 218m².
Explanation:To find the surface area of a triangular prism, we need to find the sum of the areas of all its faces.
A triangular prism has two triangular bases and three rectangular lateral faces. Let's calculate the surface area:
1. The area of each triangular base can be found using the formula: 1/2 × base × height.
For the first base, the base is 10m and the height is 6m. So the area of the first base is 1/2 × 10m × 6m = 30m².
Similarly, for the second base, the base is 9m and the height is 8m.
So the area of the second base is 1/2 × 9m × 8m = 36m².
2. The area of each rectangular lateral face can be found using the formula: length × width.
The lengths of the lateral faces are 10m, 9m, and 6m.
The common width of the lateral faces is the height of the prism, which is 8m.
So the total area of the lateral faces is 10m × 8m + 9m × 8m + 6m × 8m = 152m².
3. Finally, the total surface area of the triangular prism is the sum of the areas of the bases and the lateral faces: 30m² + 36m² + 152m² = 218m².
Therefore the surface area of a triangular prism is 218m².
The circumference of a circle is 6.28 meters. What is the circle's radius?
also how do i know
I'm having so much trouble with this one problem can you please help me so that I don't get in trouble for not having it done.
The line plot shows what fraction of a mile 13 students ran during their fitness test. What is the sum of the shortest distance a student ran and the longest distance a student ran?
The sum of the shortest distance a student ran and the longest distance a student ran is 11/8
What is a fraction?A fraction represents equal parts of a whole, by dividing it up into equal partitions. Each fraction has a numerator and denominator. The denominator represents the total number of parts the whole has been divided into.
Given is a line plot, describing the distances that is a fraction of a mile, 13 students ran during their fitness test, we need to find the sum of the shortest distance a student ran and the longest distance a student ran,
Here, according to the graph, the shortest distance = 3/8 of a mile
And the longest distance = 8/8 of a mile
So, the sum = 8/8 + 3/8 = 11/8
Hence, the sum of the shortest distance a student ran and the longest distance a student ran is 11/8
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James and Connor hid one hundred ninety eggs in a field that is seventy feet long and one hundred forty feet wide. Express the ratio of eggs to square feet as a simplified fraction
A cylinder shaped juice pitcher has a diameter of 12 cm and a height of 25 cm. What volume of juice does the pitcher contain when it is 25% full? Use 3.14 to approximate pi. Enter your answer as a decimal to the tenths place in the box
Answer:
706.5
Step-by-step explanation:
Draw 4 circle shade 2 circle
find cos^-1 0.9455 to the nearest degree.
A.26 degrees
B.71 degrees
C.19 degrees
D.41 degrees
Answer:
[tex]Cos^{-1}(0.9455)[/tex] = 19 degree.
Step-by-step explanation:
Given: [tex]Cos^{-1}(0.9455)[/tex].
To find : values of [tex]Cos^{-1}(0.9455)[/tex].
Solution : We have given that [tex]Cos^{-1}(0.9455)[/tex].
[tex]Cos^{-1}(0.9455)[/tex]. =0.33166 radians
In form of degree
0.33166 radians = 19 degree.
Therefore, [tex]Cos^{-1}(0.9455)[/tex] = 19 degree.
Use the parabola tool to graph the quadratic function. f(x)=2x2+12x+16
Answer:
Step-by-step explanation:
To obtain the graph of a parabola, three data are necessary: the vertex (the vertex is the highest or lowest point of the graph corresponding to the parabola and there it is on the plane of symmetry of the parabola), the roots ( those values of x for which the expression is 0. Graphically, the roots correspond to the abscissa of the points where the parabola cuts the x-axis.) and the concavity.
Being f(x)=ax²+bx+c, you can see that, in this case, a=2, b=12 and c=16. So:
Vertex= for your calculation, [tex]xv=\frac{-b}{2*a}=\frac{-12}{2*2}[/tex], so xv=-3. Now that you know x, all you have to do is enter its numerical value into the original formula to find yv. yv=2*(-3)²+12*(-3)+16. Then yv=-2Roots: The roots are calculated using the expression: [tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]. Replacing the values that you have:[tex]x1,x2=\frac{-12+-\sqrt{12^{2}-4*2*16 } }{2*2}[/tex] Solving, you obtain x1=-2 and x2=-4Concavity: If a> 0 (positive) the parabola is concave or pointed upwards, while if a <0 (negative) the parabola is convex or pointed downwards. In this case a = 2, so the parabola opens upward, being concave.In this way, the graph shown in the attached image is obtained.
Movies are on sale for 14 the original price. If the original price is $20, which expression gives the sale price?
Answer:
20×1/4
Step-by-step explanation:
Answer:
This is super late but I want to help others who don't know the answer
Step-by-step explanation:
The answer is in the picture.
Thank me later :)
Without multiplying, determine the sign of the product (−247,634) × (183,758). A) The sign of the product is positive because a negative multiplied by a positive is a positive. B) The sign of the product is negative because a negative multiplied by a positive is a negative. C) The sign of the product is negative because the first number is negative. D) The sign of the product is positive because the second number is positive.
Answer:
The sign of the product is negative because a negative multiplied by a positive is a negative.
Step-by-step explanation:
Without multiplying, determine the sign of the product (−247,634)(183,758).
The sign of the product is positive because a negative multiplied by a positive is a positive.
The sign of the product is negative because a negative multiplied by a positive is a negative.
The sign of the product is negative because the first number is negative.
The sign of the product is positive because the second number is positive.
This is correct because The sign of the product is negative because a negative multiplied by a positive is a negative.
PLEASE HELP ME I BEG YOU PLEASE
If y varies inversely as x, find the constant of variation if y = 36 when x = 9.
27
14
324
4
Write an appropriate direct variation equation if y = 30 when x = -10.
y = -300x
y = 300x
y = -3x
y = 3x
Write an appropriate direct variation equation if y = 14 when x = -14.
y = 14x
y = -14x
y = x
y = -x
If y varies inversely as x, and y = 4 as x = 8, find y for the x-value of 2.
16
10
8
14
Ms. Albero decided to make juice to serve along with the pizza at the Student Government party. The directions said to mix 2 scoops of powdered drink mix with a half a gallon of water to make each pitcher of juice. One of Ms. Albero’s students said she will mix 8 scoops with 2 gallons of water to get 4 pitchers. How can you use the concept of proportion to decide whether the student is correct?
As long as the amount of water is proportional to the number of scoops of drink mix, then the second quantity, amount of water, can be determined by multiplying the first quantity by the same constant. In this case, if the amount of powdered drink mix is represented by
if there are 7 hot dogs in a pound, how many pounds would you buy for a picnic to supply 28 people with two each
Which expressions are equal to 6^3 4^1/4^3 HELP ME ASAP PLEASE
We will be using division property of exponents.
The property is as follows:
[tex] \frac{x^{a}}{x^{b}} =x^{a-b} [/tex]
This means if we have same base in both numerator and denominator, the exponents will get subtracted.
In our question we have
[tex] \frac{4^{1}}{4^{3} } =4^{1-3} [/tex]
[tex] \frac{4^{1}}{4^{3} } =4^{-2} [/tex]
Now we will use another property of exponents here:
[tex] x^{-a} =\frac{1}{x^{a} } [/tex]
So if we take reciprocal of the above expression we will get,
[tex] 4^{-2} =\frac{1}{4^{2} } [/tex]
Rewriting the final answer:
[tex] \frac{6^{3} }{4^{2} } [/tex]
What is unique about Pythagorean triples? A The squares of the three sides add up to 100. B The length of each side is a perfect square. C The length of each side is a whole number. D The squares of the three sides are multiples of 3.
Final answer:
Pythagorean triples are sets of three whole numbers that form the sides of a right triangle and satisfy the Pythagorean theorem, a² + b² = c².
Explanation:
Pythagorean triples are unique because they consist of three whole numbers that satisfy the Pythagorean theorem.
Specifically, the squares of the two shorter sides (a and b), when added together, equal the square of the longest side (the hypotenuse, c). That is, a² + b² = c² holds true for these numbers.
Answering the student's question, the characteristic that is unique about Pythagorean triples is: C) The length of each side is a whole number.
This means that all three sides of the right triangle are integers, which is helpful in various mathematical and practical applications. Examples of Pythagorean triples include (3, 4, 5) and (5, 12, 13).
Simplify expression: (5^3)^3
find the volume of the same prism
1. 64,288 ft3
2.1,312 ft3
3. 2,009 ft3
4.23,208
A container holds 8 gallons of water. If 4 5 of a gallon is added to the container each hour, how many hours would it take to fill the container?
Which of the follow is true about the expression Sqrt 3 * sqrt 2
A) It represents the product of two irrational numbers and is equivalent to a rational number.
b) It represents the product of two irrational numbers and is equivalent to an irrational number.
C) It represents the product of two rational numbers and is equivalent to a rational number.
D)It represents the product of two rational numbers and is equivalent to an irrational number.
Answer:
A
Step-by-step explanation:
Find the fraction that is equivalent to 1/4
divide (3x^3+5x) by (x+3)
Draw a number line that shows two equivalent fractions.label your number line and explain how you know the fractions are equivalent.
which is a valid conclusion that can be drawn from these statements
The glass fish tank does not have a cover. Find the total area of the glass panels used to make the tank.
plz help thank you
does the equation x2 +12x +3=136 have the same solutions as the equation (x+6)2=169
need help plz Noah, some one
Use tens to solve 13-7
Paul has a piece of wood that is 4 yards long. He knows there are 12 inches in 1 foot, and 3 feet in 1 yard. If there is no wood left over, how many 6-inch pieces can Paul cut from the length of wood? Remember to include units! (Example: 18 6-inch pieces)
24 Pieces cut from the wood.
What is a simplified Fraction?Simplest form conversion of incorrect fractions to mixed numbers. By reducing to the simplest words and outlining the effort required, this calculator also makes correct fractions simpler. A number that will divide equally into the numerator and denominator so that it may be lowered is required in order to simplify a fraction. To transform a fraction into a mixed number, the numerator must be higher than the denominator (an improper fraction).
Given, Paul has a piece of wood that is 4 yards long. He knows there are 12 inches in 1 foot, and 3 feet in 1 yard. total woods in inches would be,
total inches of wood = 4 yards
total inches of wood = 4 * 3 feet
total inches of wood = 4 * 3* 12 inches
total inches of wood = 144 inches
Given 6-inch pieces cut from the length of the wood. Therefore, the total number of pieces cut from the wood is 144/6 or 24 pieces
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Which of the following points lies on the graph of the line y = 5x - 2
A. (0,4)
B. (2,8)
C. (-1,2)
D. (4,10)
The point (2, 8) lies on the line y = 5x - 2 which is correct option(B).
What is the graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
To determine the point lie on line or not we have to put points in equation if it satisfy then it lie otherwise not.
(A) Point (0, 4)
y = 5x - 2
Substitute x = 0 and y = 4,
4 = 5(0) - 2
4 = -2
Point (0, 4) does not lie on the line.
(B) Point (2, 8)
y = 5x - 2
Substitute x = 2 and y = 8,
8 = 5(2) - 2
8 = 10 - 2
8 = 8 True
Point (2, 8) lies on the line.
(C) Point (-1,2)
y = 5x - 2
Substitute x = -1 and y = 2,
2 = 5(-1) - 2
2 = -7
Point (-1,2) does not lie on the line.
(D) Point (4,10)
y = 5x - 2
Substitute x = 4 and y = 10,
10 = 5(4) - 2
10 = 18
Point (4,10) does not lie on the line.
Hence, the point (2, 8) lies on the line.
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