Example
we have
\(\sqrt{\frac{25}{4}}\)This is the same that
\(\sqrt{\frac{25}{4}}=\frac{\sqrt{25}}{\sqrt{4}}=\frac{5}{2}\)ON Answe
a. Without using mathematical table or calculator, simplify.
1271
Answer:
Step-by-step explanation:
1271 = 31 *41
31 and 41 are prime number.
Find the distance between point P and line L
The distance between point P and line L is 16/9√(13).
To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:
Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:
|ax1 + by1 + c|/√(a² + b²)
To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.
2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y
The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:
y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4
Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.
Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).
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a 16 foot ladder leans against a building. if the angle the ladder makes with the ground is 68°, how high up the building does the ladder read?
Answer:
14.8
Step-by-step explanation:
i got it right
The ladder will reach up to 14.83 feet high up the building.
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle.
Given that, a 16-foot ladder leans against a building. if that angle the ladder makes with the ground is 68°,
This situation creates a structure like a right-angled triangle, (refer to the figure attached) and we know that in a right-angled triangle, the sine of one of the angles of a right triangle is the ratio of the length of the side of the triangle opposite the angle to the length of the triangle's hypotenuse
sin 68° = x/16
x = sin 68°×16
x = 14.83 ft
Hence, The ladder will reach up to 14.83 feet high up the building.
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sandy pays $120 for 4 violins lessons how much does she pay for 1 violin lesson?
Answer:
$30 is the right answer of the cost of 1 violon
What the meaning of statement this?
The statement "Every set can be considered a class" means that every object in set theory, including sets, can be considered a class. This is because classes are simply collections of objects, and sets are a type of collection.
What does the statement implies?The statement "If S is a set, consider the formula x S and the class {x: x = S}" means that if S is a set, then we can consider the formula x S, which states that x is an element of S, and the class {x: x = S}, which is the class of all objects that are equal to S.
In other words, the statement is saying that every set can be considered a class, and that we can define a class for any set by considering the formula that defines the set and the class of all objects that satisfy that formula.
For example, the set {1, 2, 3} can be considered a class by considering the formula x ∈ {1, 2, 3}, which states that x is an element of the set {1, 2, 3}, and the class {x: x ∈ {1, 2, 3}} is the class of all objects that are elements of the set {1, 2, 3}. This class is equal to the set {1, 2, 3}.
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After birth, a baby's weight increased at a steady rate for several weeks.
A linear model of this situation contains the values (1, 7.3) and (9, 9.7), where x represents the number of weeks, and y represents the baby's weight, in pounds.
What was the baby's weight at birth?
A.
8 pounds
B.
7.3 pounds
C.
0.3 of a pound
D.
7 pounds
Answer:
c
Step-by-step explanation:
i really dont know pls help PAHAHA
The baby's weight at the birth of the baby was 7 pounds.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a linear model of this situation contains the values (1, 7.3) and (9, 9.7), where [x] represents the number of weeks, and [y] represents the baby's weight, in pounds.
Assume the equation of the line in slope - intercept form is -
y = mx + c
Now -
m = (9.7 - 7.3)/(9 - 1)
m = 2.4/8
m = 0.3
The equation will be -
y = 0.3x + c
For the point - (1, 7.3), we can write -
7.3 = 0.3 x 1 + c
c = 7.3 - 0.3
c = 7
Therefore, the baby's weight at the birth of the baby was 7 pounds.
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Write 0.000299 in scientific notation
Answer:
0.000299 in scientific notation
2.99 × 10-4
Step-by-step explanation:
To convert 0.000299 into scientific notation also known as standard form, follow these steps:
Move the decimal 4 times to right in the number so that the resulting number, m = 2.99, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -4
Write in the scientific notation form, m × 10n
= 2.99 × 10-4
Answer:
0.000299
2.99 × 10^-4.
Step-by-step explanation:
15 cm
5 cm
4 cm
3 cm
Find the lateral surface area of the solid above.
Answer here
The answer for lateral surface area of the Triangular prism is 180 cm²
What is Lateral Surface Area?Any solid object's lateral area can be calculated using the lateral area formula. Any figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as the cuboid, cube, cylinder, cone, and sphere, is made easier using lateral area formulas.
The lateral area for a triangular prism
A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Additionally called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.
The total of the three regions is the triangular prism's lateral area. Consequently, the triangular prism's lateral area formula is
Triangular prism lateral surface area (LSA) = ah + bh + ch (or) (a + b + c) h.
We are aware that the perimeter of the base is (a + b + c) (triangle). Hence,
Triangular prism's lateral surface area (LSA) is equal to the product of the base's perimeter and the prism's height.
base perimeter × height
Explanation
The Given Image of the solid is Matching to a prism.so we are calculating the lateral surface area of the prism
The dimensions of each base are:
a = 5cm
b = 4 cm
c = 3 cm
The height of the triangular prism = 15cm.
Thus, the lateral area of triangular prism = (a + b + c ) h
= (5 + 4 + 3) 15
= (12) 15
= 180 cm²
Answer: The lateral area of the given triangular prism = 180 cm²
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Consider the following expressions: A. 34÷23 B. 710÷45 C. 78÷12 D. 34÷13 E. 15÷1115 a. Which expression(s) will result in a quotient that is greater than one? 34÷23 710÷45 78÷12 34÷13 15÷1115
Answer:
A, B, C, and D
Step-by-step explanation:
What fraction of the circle would 3 pieces represent?
Answer:
3/4 would represent the shaded in parts of the circle
Step-by-step explanation:
I cannot give you an accurate answer seeing as you did not give much detail
Which expression equals 5^0
Answer:
\( {5}^{0} = 1\)
**Every number to the exponent zero equals one .
I hope I helped you^_^
I need help on it pls pls
Answer:
b,d
Step-by-step explanation:
The ratio of two numbers is 5 to 6. If their sum is 88, what is the value of the smaller number?
Answer:
The smaller number is 40.
Step-by-step explanation:
The divisor is 5 + 6 = 11.
So one part = 88/11 = 8
So we need to find 5 parts and 6 parts.
The 2 numbers are:
5 * 8 = 40 and
6 * 8 = 48.
Donna finished 67% of her homework. What fraction of her homework is
completed?
67/10
0.67/100
67/100
67/1000
Answer:
67/100
Step-by-step explanation:
Percent means out of 100.
67% = 67/100
Answer:
67/100
Step-by-step explanation:
When we say Donna has completed 67% of her homework, we are referring to a percentage, which is a way of expressing a part out of 100. In this case, the percentage is 67%.To convert a percentage to a fraction, we can simply write the percentage as a fraction with 100 as the denominator. In this case, since the percentage is 67%, the fraction would be 67/100.\(67\%=\dfrac{67}{100}\)$39,100 $39,300 $43,700 $23,900 $38,500 $30,600 the mean annual salary is $ ????
Answer: 35,850
Step-by-step explanation:
just add all your numbers and divided by how many numbers you got.
if the radius of the base is 2 cm and the height is 24cm what is the volume?
If Jim Roller can paint a room in 3 hours while John Brush would take 5 hours, how long will they take if they work together? 1/8 hour 8/15 hour 1 7/8 hours
Answer:
Step-by-step explanation:
Each hour, Jim does 1/3 of the job if working alone.
Each hour, John does 1/5 of the job if working alone.
Let x = number of hours to do the job if they work together. So, each hour, they do 1/x of the job when they work together.
We get the equation: 1/3 + 1/5 = 1/x
Multiply the equation by the LCD, 15x: 5x + 3x = 15
8x = 15
x = 15/8 = 1 7/8 hrs
ANSWER: (C).
50 Points! Multiple choice algebra graphing question. Which square root function is represented by the graph? Photo attached. Thank you!
A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).
What is a square root function?In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.Therefore, the required square root function is given by;
f(x) = √(4x + 8)
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The conditional statement below is true. If possible, write the biconditional statement.
If 2x = 18, then x = 9.
The biconditional statement for the given conditional statement would be:
2x = 18 if and only if x = 9.
The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".
To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.
If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.
Based on this, we can write the biconditional statement:
2x = 18 if and only if x = 9.
The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.
In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.
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a function f from a to b is a relation from a to b that satisfies two properties: for every xelement of a, there is a y element of b such that element of f for all elements x element of a and both y and z such that y element of b and z element of b: if (x,y) and (x,z) are in f, then
A relation from A to B is a function if it satisfies two properties:
For every x ∈ A, there is a y ∈ B, such that (x,y) ∈ FFor all elements x ∈ A and both y and z such that y ∈ B and z ∈ B, if (x,y) and (x,z) are both in F, then y = z.Suppose we have two sets A and B and we have a relation that maps elements of A to elements of B. A relation from A to B is defined as a function if every elements of A is related to exactly one element of B.
Let (x,y) is a pair of input and output. If (x,y) is related by a function f, we can denote (x,y) ∈ F
We can write the first condition as:
For every x ∈ A, there is a y ∈ B, such that (x,y) ∈ FSince x is mapped to the exactly one output, then if both y and z are elements of B and (x,y) and (a,z) are in F, then y must be equal to z. Hence, the second condition is:
2. For all elements x ∈ A and both y and z such that y ∈ B and z ∈ B, if (x,y) and (x,z) are both in F, then y = z.
There are typos in your question. Most likely your question was like on the attached picture:
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Simplify the following expression: 9 – 3x + (-6x) + 4
Answer:
-9x + 13
Step-by-step explanation:
9 -3x +(-6x) +4
you will add -3x+(-6x), then add 9+4
-3x+(-6x) = -9x (a negative pus and negative = a negative
9 +4 = 13
-9x + 13
SA = 2πr2 + 2nrh
(Use 3.14 for pi.)
Jill needs wrapping paper
for a cylindrical gift that is
10 inches high and measures
4 inches across the base.
How much wrapping paper
will she need?
square inches
Do NOT round your answer.
Work Shown:
\(\text{SA} = 2\pi*r^2 + 2\pi*r*h\\\\\text{SA} \approx 2*3.14*2^2 + 2*3.14*2*10\\\\\text{SA} \approx 150.72\\\\\)
She'll need approximately 150.72 square inches of wrapping paper.
Note: The circular base is 4 inches across, which is the diameter. Cut this in half to get r = d/2 = 4/2 = 2 inches for the radius.
Based on the graph, which inequality is correct for a number that is to the right of -4?
A number line is shown from negative 8 to 8 at increments of 1. A circle is shown at negative 4. The entire portion of the number line to the right of negative 4 is shaded.
2 < −4
Answer:
yo- ehm I think itssss 2 > -4
Step-by-step explanation:
7f-9>3f-1 please show work
Answer:
f > 2
Step-by-step explanation:
7f-9 > 3f-1 subtract 3f from both sides
4f-9 > -1 add 9 to both sides
4f > 8 divide 4
f > 2
NO LINKS!! Help me with the 2-Column Proof Part 3aa
Here is the two column proof:
Statement Reason
RD bisects OS GivenA is the point of intersection Shown on the diagramOA ≅ AS Definition of a segment bisectorProved
what's the end behavior of: y= 2 + log2(x - 1)
We can infer that the function y = 2 + log2(x - 1) has the following final behaviour:
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.what is a function?A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input. Y = f is a common way to represent a function (x).
A function in mathematics is a certain configuration of the inputs (also known as the domain) and their outputs (also known as the codomain), where each input has precisely one output and the output can be connected to its input.
from the question;
We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behaviour of the function
y = 2 + log2(x - 1).
The formulas (x - 1) and log2(x - 1) also approach infinity as x gets closer to positive infinity. As a result, y increases as x moves closer to positive infinity. The following can be written:
lim x→∞ 2 + log2(x - 1) = ∞
Expression (x - 1) moves closer to zero and log2(x - 1) moves closer to negative infinity as x moves towards 1 from the right. So, as x moves closer to 1 from the right, y moves closer to negative infinity. The following can be written:
lim x→1+ 2 + log2(x - 1) = -∞
This leads us to the following conclusion about the final behaviour of the function y = 2 + log2(x - 1):
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.to know more about the function visit:
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Solving a word problem on proportions using a unit rate
Dante drove 871 miles in 13 hours.
At the same rate, how long would it take him to drive 603 miles?
please help me with this thank you
(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.
(10) The slope of a line parallel to this line, y = 10 -8x is -8.
What is the slope of a line perpendicular to the line?The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.
Question 9.
f(x) = 0.75x + 6
where;
0.75 is the slope of the line6 is the interceptThe slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3
Question 10.
For the equation of another line, y = 10 - 8x
The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;
y = 10 - 8x
where;
-8 is the slope10 is the y interceptslope of a line parallel to the line = -8
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Let Aequals [Start 2 By 2 Matrix 1st Row 1st Column 3 2nd Column 2 2nd Row 1st Column negative 1 2nd Column 2 EndMatrix ]and Bequals [Start 2 By 2 Matrix 1st Row 1st Column 2 2nd Column 6 2nd Row 1st Column negative 3 2nd Column k EndMatrix ]. What value(s) of k, if any, will make ABequals BA?
Answer:
No value of k will make AB=BA
Step-by-step explanation:
\(A=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right), $ $B=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right) \\\\\\AB=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)=\left(\begin{array}{ccc}3*2+2*-3&3*6+2*k\\-1*2+2*-3&-1*6+2k\end{array}\right)=\left(\begin{array}{ccc}0&18+2k\\-8&-6+2k\end{array}\right)\)
\(BA=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)=\left(\begin{array}{ccc}0&16\\-6&-6+2k\end{array}\right)\)
We can see that \(AB \neq BA\). Therefore, there is no value of k that will make it equal. In general, matrix multiplication is not commutative.
Question
A data set is summarized in the frequency table
below. The data set contains a total of 40 data
values. What is the missing frequency?
Value
1
2
3
4
Cr
5
6
7
8
Frequency
2
4
9
[]
6
8
2
4
The required Missing Frequency is 3.
What is frequency ?Frequency is a measure of the number of occurrences of a given event within a specified period of time. It can refer to the number of times a particular event happens in a unit of time.
Such as the number of times a wave or vibration occurs in a second, or the number of times an action occurs in a given period. In physics, frequency is measured in hertz (Hz); in electrical engineering, it is measured in cycles per second (cps). Frequency is also used in mathematics, music, and sound engineering.
Value Frequency
1 2
2 4
3 9
4 ?
5 6
6 8
7 2
8 4
Total 40
We have to find the Missing frequency:
Computation:
Missing frequency = Total frequency - Counted
Missing frequency = 40 - 37
Missing frequency = 3
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