The expression for adding 8 to the sum of 23 and 10 is (23 + 10) + 8. This is due to the commutative property of addition, which states that the order in which you add numbers does not change the result.
Explanation:The question asks for an expression to calculate adding 8 to the sum of 23 and 10. The first step is to add 23 and 10 together, which equals 33. Then add 8 to that sum. You can represent this process mathematically as (23 + 10) + 8. So if you need to write an expression for adding 8 to the sum of 23 and 10, it would be (23 + 10) + 8. Remember, adding numbers together (a process called addition) is commutative, meaning you can add numbers in any order and still get the same result.
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What is the value of 324?
15 POINTS. What is the area of the circle segment/shaded area? Picture included please help. Please answer in a way that will fill in the blanks, explanation preferred.
To find the area of a circle segment, you need to know the radius and central angle of the segment. Use the formula Area of Circle Segment = ((central angle/360) x πr²) - 0.5r²sin(central angle) to calculate the area.
Explanation:To calculate the area of the segment or shaded area of a circle, you must first need to know the radius of the circle and the central angle of the segment, as these will be necessary for the calculation. The formula for calculating the area of a segment in a circle is Area of Circle Segment = ((central angle/360) x πr²) - 0.5r²sin(central angle).
For instance, if the circle has a radius of 5 cm and the central angle of the segment is 60 degrees, the area is ((60/360) x π5²) - 0.5 x 5²sin(60), which will give the result when evaluated.
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graph the function g (x)=1/3-4/3x
Prove that a triangle cannot have two right angles.
A triangle cannot have two right angles. Suppose a triangle had two right angles.
A triangle cannot have two right angles because the sum of the interior angles in any triangle is equal to two right angles. Having two right angles would necessitate that the third angle also be a right angle, forming a straight line instead of a triangle.
Proof that a Triangle Cannot Have Two Right Angles
The notion that a triangle cannot have two right angles is fundamentally rooted in the geometry axiom stating that the sum of the interior angles in any triangle is equal to two right angles (or 180 degrees). If a triangle were to have two right angles, the third angle would also have to be a right angle to satisfy the sum of 180 degrees. However, if the third angle is a right angle, this contradicts the definition of a triangle being a three-sided polygon with three angles that add up to 180 degrees; with three right angles, the figure would no longer be a triangle, as the three lines AC, CD, and BD would line up to form a straight line, eliminating the closed polygon structure of a triangle.
If we consider the work of notable mathematicians such as Legendre and Dehn, we find substantial evidence supporting the statement that the sum of the interior angles of a triangle cannot be greater than two right angles. Legendre's attempts to prove this led to understanding the consistency of triangle angle sums across all triangles; that is, if one triangle's angles added up to two right angles, it would be the same for all triangles. Furthermore, Dehn's hypothesis indicated that without parallel lines, the sum of the angles of a triangle is greater than two right angles.
Overall, every triangle must have at least two acute angles, and any attempt to form a triangle with two right angles would result in a shape that does not adhere to the fundamental properties of a triangle.
p varies directly as q. When q = 31.2, p = 20.8. Find p when q = 15.3.
a.10.2
b.22.95
c.42.4
i got B ...?
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem we have
[tex]p=20.8\\q=31.2[/tex]
Find the value of k
[tex]k=q/p[/tex]
Substitute the values
[tex]k=31.2/20.8[/tex]
[tex]k=1.5[/tex]
The linear equation is
[tex]q=1.5p[/tex]
For [tex]q=15.3[/tex]
Find the value of p
Substitute in the linear equation and solve for p
[tex]15.3=1.5p[/tex]
[tex]p=15.3/1.5=10.2[/tex]
therefore
the answer is the option a
[tex]10.2[/tex]
if a can is 12cm high and 8cm wide how much milk can it hold
Final answer:
To find the volume of a cylindrical can, one must apply the formula for volume of a cylinder, V = πr²h, with the given dimensions. The can's volume is approximately 603.19 cubic centimeters or milliliters, translating to about 0.603 liters.
Explanation:
The student is asking about the volume of a can, which is the measure of how much space it occupies or, in this context, how much liquid it can hold. To find the volume of a cylindrical can, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Since the can is 12 cm high and 8 cm wide (which is the diameter), the radius would be 4 cm (which is half of the diameter). Substituting these values into the formula gives us V = π(4cm)²(12 cm), which simplifies to V = π × 16 cm² × 12 cm). When calculated, the volume of the can is approximately 603.19 cubic centimeters.
Since the student may also be interested in capacity in terms of common liquid measurements, it is useful to know that 1 cubic centimeter is equivalent to 1 milliliter.
Thus, the can would be able to hold approximately 603.19 milliliters. Given that 1000 milliliters make up 1 liter, the can's capacity would be roughly 0.603 liters, which is a little over half a liter.
Please answer !!!the system of equations graphed below has how many solutions ?
A. infinitely many
B. 1
C. 0
D.2
Solve the exponential equation
9^2x = 27
Answer:
The value of x is, [tex]\frac{3}{4}[/tex]
Explanation:
Given:
The exponential equation [tex]9^{2x} =27[/tex] ....[1]
Exponential Identities:
[tex](x^a) =x^{ab}[/tex]
we can write equation [1] as;
[tex](3^2)^{2x} = 3^3[/tex] [ [tex]3 \times 3= 9 , 3 \times 3 \times 3 = 27 [/tex] we can rewrite as [tex]3^2 =9 , 3^3 =27[/tex]]
by using above identities, we have
[tex](3)^{4x} = 3^3[/tex] then,
[tex]4x =3[/tex] [ if [tex]x^a =x^b[/tex] then a =b]
Simplify:
[tex]x = \frac{3}{4}[/tex]
Find the value of the function when n = 7. p = 0.006n
a. 0.0078
b. 0.042
c. 0.42
d. 7.006
what is the answer to this problem 452q=39,324 ?
Translate this sentence into an equation.
The product of Matt's score and
6
is
96
.
Use the variable
m
to represent Matt's score.
Final answer:
The sentence 'The product of Matt's score and 6 is 96' translates to the equation m × 6 = 96. By dividing both sides by 6, the value of Matt's score, denoted as m, is found to be 16.
Explanation:
To translate the given sentence into an equation, you start by identifying the mathematical operation described. The sentence states 'The product of Matt's score and 6 is 96'. The word 'product' indicates multiplication. Next, you use the variable m to represent Matt's score.
The equation that represents this situation is:
m × 6 = 96
To solve for m, you divide both sides of the equation by 6:
m = 96 ÷ 6
m = 16
Therefore, Matt's score is 16.
6/7 times 4/5 times 35
1.) If 60% of a number is 18, what is 90%of the number?
A.)3
B.)16
C.)27
D.)30
2. Taryn's grandma took her family out to dinner.If the dinner was $74 and Taryan's dinner was 20% of the bill, how much was Taryn's dinner?
A.$6.80
B.$7.20
C.$9.50
D.$14.80
PLEEEEEEEEASE HELP! How the heck do i figure this out!!!?
Find m
The function f(x)=5000(0.98)^0.3x
represents the number of white-blood cells, per cubic millimeter, in a patient x days after beginning treatment for a virus.
What is the average decrease per day in white-blood cells per cubic millimeter between days 1 and 5?
a.) −29.75 mm^3/day
b.)-34.75 mm^3/day
c.)-282.47 mm^3/day
d.-)353.08 mm^3/day
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above.
F(x, y, z) = xyi + 5zj + 7yk, C is the curve of intersection of the plane x + z = 8 and the cylinder x2 + y2 = 9.
Find the surface area and volume of a sphere having a radius of 4"
During a football game, a team lost 9 yards on the first play, then gained 3 yards on each of the next 3 plays. Which integer represents the total number of yards at the end of the first four plays? –3 0 9 18
Answer:
0
Step-by-step explanation:
Team infinite dimensions canoed 15 3/4 miles in 3 hours. what was their average rate of speed in miles per hour?
On a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?
A.) 1.5 feet and 3.5 feet
B.) 1.4 feet and 4 feet
C.) 3.5 feet and 4 feet
D.) 4 feet and 4 feet
The laser will cut the archway at height of 3.5 feet and 4 feet (Option C).
Equating the parabolic and Linear Equation?A linear equation exists an equation in which the highest power of the variable stands always 1. It exists also known as a one-degree equation. The standard form of a linear equation in one variable exists in the form Ax + B = 0. Here, x is a variable, A exists as a coefficient and B is constant.
A parabola exists as a plane curve that stands mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be proved to determine exactly the same curves.
Refer to the following figure:
The blue line represents eqn of archway: y = -0.5x^2 + 3x, and green line represent eqn of laser: -0.5x + 2.42y = 7.65.
Now to find out the points at which laser cuts archway, we need to equate both the eqns.
[tex]-0.5x^{2} +3x=\dfrac{7.65+0.5x}{2.42}[/tex]
[tex]-1.21x^{2} +7.26x=7.65+0.5x[/tex]
[tex]-1.21x^{2} +6.76x-7.65[/tex]=0
On solving the quadratic eqns, we get x =3.5 and 4 (approximate)
Therefore, point A and B are 3.5 and 4 feet respectively.
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When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?
Multiply each side by negative one over eight , add 35 to each side
Multiply each side by negative one over eight , subtract 35 from each side
Multiply each side by −8, subtract 35 from each side
Multiply each side by −8, add 35 to each side
Dan counted all the coins in his bank, and he had 72 quarters. can he exchange the quarters for an even amount of dollar bills? how do you know?
In this triangle, the product of sin B and tan C is _____ , and the product of sin C and tan B is _______.
Answer
part 1 = c/a
part 2 = b/a
Sine is the ratio of opposite to hypotenuse respect to as a given angle while tangent is the ratio of opposite to adjacent lengths of a given angle.
Part 1
Sine = opposite/hypotenuse
SinB = b/a
Tangent = opposite/adjacent
TanC = c/b
SinB × TanC = b/a×c/b
= c/a
Part 2
SinC = c/a
TanB = b/c
SinC×TanB= c/a×b/c
= b/a
How do you write 6.8 as a fraction?
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction.
Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"? (Hint: cross products)
Answer: 4n + 12 = 3d
Step-by-step explanation:
The equation representing "If the numerator of a fraction is increased by 3, the fraction becomes 3/4" is 4(x + 3) = 3y. This, alongside the second condition of the denominator decreased by 7 leading to the fraction becoming 1, provides two equations that can be solved for the original fraction.
Explanation:To represent the situation "If the numerator of a fraction is increased by 3, the fraction becomes 3/4," we can use the variable x for the numerator and y for the denominator of the original fraction. Therefore, the equation would be (x + 3)/y = 3/4. Applying the cross-product rule, we multiply each side of the fraction by the denominator on the other side, leading to 4(x + 3) = 3y. Simplified, this equation is 4x + 12 = 3y, which helps us solve for the original fraction along with the other given condition that reducing the denominator by 7 makes the fraction equal to 1. So, the second condition can be written as x/(y - 7) = 1. These two equations together can be solved simultaneously to find the values of x and y.
Jeff collects toy cars. they are displayed in a case that has 4 rows. there are 6 cars in each row. how many cars does jeff have?
if 5a = 20b, then b/a=
A. 4
B. 1/4
C. 4/1
D. 10
The ratio b/a is found by dividing both sides of the equation 5a = 20b by 5a, resulting in b/a being B) 1/4.
The question asks us to solve for the ratio b/a given the equation 5a = 20b. To find b/a, we can divide both sides of the equation by 5a:
5a = 20bFrom this, we can see that b/a must be 1/4, since 4 multiplied by 1/4 equals 1. Therefore, the correct answer is B. 1/4.
Does the equation y = (0.9)x represents exponential growth or decay?Answer
Exponential Growth
Exponential Decay
Exponential decay is demonstrated in the equation y = (0.9)x, showcasing a decrease as x increases.
Exponential decay occurs when the base of the exponential function is between 0 and 1, causing the function to decrease as x increases.
For example, if x = 1, y = 0.9; if x = 2, y = 0.81; and so on.
A secretary at the police department makes $8 less per hour than the dispatcher. The combined hourly wage of the secretary and the dispatcher is $40. Which equation could be used to find the hourly wage of the dispatcher?
A certain forest covers an area of 5000km^2 . Suppose that each year this area decreases by 5.75% . What will the area be after 14 years?
...?
The forest with an area of 5000 km² decreases by 5.75% annually. After 14 years, the forest area will be approximately 2,182 km².
The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest.
The compound interest formula is:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A is compounded amount
P is principal amoutn
r is the rate of interest
n is the number of times it is compounded
Given that,
Initial forest area (P): 5000 km²
Rate of decrease per year: 5.75% or 0.0575
Number of years (n): 14
Since the area is decreasing,
Therefore r = -0.0575
Plugging in the values in the compound interest formula,
[tex]A = 5000 \times (1 - 0.0575)^{14} \\\\\approx 2,182 \text{ square km}[/tex]
Hence,
After 14 years, the forest area would be approximately 2,182 km².
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