angles in a triangle = 180 degrees
70 +35 = 105 degrees
180-105 = 75 degrees
3rd angle = 75 degrees
Peter decides to mix grades of gasoline in his truck. He puts in 11 gallons of regular and 7 gallons of premium for a total cost of $76.99. If premium gasoline costs $0.25 more per gallon than regular, what was the price of each grade of gasoline?
Final answer:
Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.
Explanation:
We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.
Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:
11r + 7(r + $0.25) = $76.99r = regualar gasoline price per gallonSimplifying the first equation:
11r + 7r + $1.75 = $76.99
18r + $1.75 = $76.99
18r = $76.99 - $1.75
18r = $75.24
r = $75.24 / 18
r = $4.18
So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.
The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 25 feet. Round your answer to the nearest tenth.
In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide
In a glide reflection, the reflection comes first and the glide comes second.
Explanation:In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.
Learn more about Glide reflection here:https://brainly.com/question/2254222
#SPJ12
A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?
Write 935.97 in expanded form
How do I answer this question?
a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, how many miles from earth is the star?
In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]
How can the number of miles be calculated?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that star=3.4 light years from earth
1 light years= [tex]5.87*10x^{12} miles[/tex]
The number of miles from earth is
[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]
Learn more about number at
https://brainly.com/question/24644930
#SPJ2
What is the area of a parallelogram with a base of 20 inches and an altitude of 8 inches?
The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.
What is a parallelogram in math?
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.
Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
A = base * altitude
A = 20 * 8
A = 160 inches square.
learn more about the area here https://brainly.com/question/25965491
#SPJ2
If using spss, what is the exact likelihood of obtaining a t-test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true
Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.
To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.
What are the counting numbers in base 6
In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1 one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we would need:
Base 6 Base 10
1 1
2 2
3 3
4 4
5 5
10 (1 six plus 0 ones) 6
11 (1 six plus 1 one) 7
12 (1 six plus 2 ones) 8
13 9
14 10
15 11
20 (2 sixes plus 0 ones) 12
21 (2 sixes plus 1 one) 13
22 14
23 15
Final answer:
The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.
Explanation:
The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.
The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.
Write 337,060 in expanded form using exponents
what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4
Answer:
A on Edge 2021
[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]
In a circle of radius 25 inches, a central angle of 35 degrees will intersect the circle forming an arc of length ____
arc length = (central angle/360) x 2 x PI x r
= (35/360) x 2 x 3.14 x 25
=15.2638
round answer as needed, you don't say how to round it.
how do write an equation to represent a real world situation?
2^-1 ∙ 2^-4 is what?
Which if the following is the smallest value 0.79, 2.40, 3.00007, 0.424, or 100?
What is the next number of 2 7 8 3 12 9
Answer with Step-by-step explanation:
We are given a pattern
2 7 8 3 12 9
and we are asked to find the next term of this pattern
2+1=3
7+5=12
and 8+1=9
We can view this pattern in the set of three numbers and then, the next three are formed by adding one, five & one, respectively.
See these COLUMNS of groups of three:
2 3 4
7 12 17
8 9 10
Hence, next number in the pattern is:
4
Which of the following is a polynomial with roots negative square root of 5, square root of 5, and −3?
x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15
this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box
Answer:
48 cubic meters.
Step-by-step explanation:
48x1
unit meter is cubic meters
Write the quadratic function in the form g(x)= a (x-h)^2 +k . Then, give the vertex of its graph. g(x)=3x^2+30x+72
Writing in the form specified: g(x)= ___
Vertex:___
ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?
Answer:
The correct answer is
C 40/41
Step-by-step explanation:
What is a ratio equivalent to 8/10 with lower terms
“the sum of eight and twice w”
Answer:
the expression is [tex]8+2w[/tex]
Step-by-step explanation:
WE need to write the expression for the given statement
“the sum of eight and twice w”
Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'
Difference represents the subtraction operation.
Sum represents the addition operation.
twice 'w' means 2 times w that is 2w
the sum of 8 and 2w
For sum we use '+'
so ,the expression becomes [tex]8+2w[/tex]
What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?
The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).
Explanation:In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:
First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).
Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.
So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).
Learn more about Coordinate Transformation here:https://brainly.com/question/37212834
#SPJ11
Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=52t-16t^2 . What is the maximum height that the ball will reach? Do not round your answer.
Height: ________Feet
The maximum height would be 42.25 feet that the ball will reach.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²
Here h(t) = 52t - 16t²
Differentiate with respect to t to get maximum height
h'(t) = 52 - 2 × 16t
h'(t) = 52 - 32t
In this position, the acceleration would be zero,
So 0 = 52 - 32t
32t = 52
t = 52/ 32
t = 1.625
Substitute the value of t = 1.625 in the given function,
⇒ h = 52(1.625) - 16(1.625)²
⇒ h = 84.5 - 42.25
⇒ h = 42.25
Therefore, the maximum height would be 42.25 feet that the ball will reach.
Learn more about Velocity here:
https://brainly.com/question/12904979
#SPJ2
Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7
A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.
Based on the historical record what is the empirical probability that the city will be hit by a tornado
Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?
Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.
Explanation:The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.
Learn more about Triangle Classification here:https://brainly.com/question/4028542
#SPJ2