Step-by-step explanation:
12 holes / 6 minutes = 2 holes / 1 minute
the simplified ratio is 2/1 = 2.
so, for 25 minutes we need to keep the same ratio :
x holes / 25 minutes = x/25 = 2
x = 2×25 = 50
it drills 50 holes in 25 minutes.
1. A taxi charges a flat rate of $1.75 plus an additional $0.65 per mile. If Eli has at most $10 to spend on the cab ride, how far could he travel?
17 miles
12 miles
23 miles
9 miles
2. Which inequality matches the statement below?
Three-fourths times x added to two times x is more than eleven
3/4x + 2 > 11
2x + 3/4x > 11
3/4(x+2) > 11
3/4 + x + 2 + x > 11
Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that a taxi charges a flat rate of $1.75 and an additional $0.65 per mile.
Eli has at most $10 to spend on the cab ride
We need to find how far could he travel
1.75+0.65x≤10
Subtract 1.75 on both sides
0.65x≤10-1.75
0.65x≤8.25
x≤8.25/0.65
x≤12.6
So he could travel 12 miles.
Three-fourths times x added to two times x is more than eleven
3/4x+2x>11
Hence, Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven
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Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Answer:
yes, the board is long enough
Step-by-step explanation:
5.5 in x 4 walls = 22 inches
The board is 24.5 in, so there is enough.
24.5 > 22, there is an extra 2.5 in left over.
What are the 4 types of real numbers?
Real numbers are every number that exists in the real line, The four types of real numbers are rational, irrational, Natural and Integers.
What is a real number?In mathematics, a real number is a value that can be represented on the number line. The set of real numbers includes both rational numbers (such as integers, fractions, and decimals) and irrational numbers (such as √2 and π). Real numbers also include positive numbers, negative numbers, and zero. The set of real numbers is usually represented by the symbol R, and it has the properties of being closed under the operations of addition, subtraction, multiplication, and division (except for division by zero).
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
Rational number = 3/4, -6/2, or 0.5.
Irrational number = √2, π, or e.
Natural number = 1,2,3,4....
Integers = -4, -1, 0, 1, 4.
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What is the HCF of the polynomials x6 3x4 3x^2 1 and x^3 3x^2 3x 1?
The HCF of the polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1 is 1
When we divide the polynomials f(x) / g(x) then we get f(x) = g(x) × q(x) + r(x). Assuming the degree of g(x) > degree of r(x).
If the remainder r(x) is zero, then q(x) is the highest common factor of polynomials.
Here, we have been given two polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1
Let f(x) = x^6 + 3x^4 + 3x^2 + 1 and g(x) = x^3 + 3x^2 + 3x + 1
We can write these polynomials as:
f(x) = x^6 + 3x^4 + 3x^2 + 1
f(x) = (x² + 1)^3
The factors of polynomial f(x) = x^6 + 3x^4 + 3x^2 + 1: 1 and (x² + 1)^3
And g(x) = x^3 + 3x^2 + 3x + 1
g(x) = (x + 1)^3
And the factors of g(x) = x^3 + 3x^2 + 3x + 1 : (x + 1)^3 and 1
Therefore, the HCF of the polynomials f(x) and g(x) = 1
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20 workers can paint a building in 21 days. If work has to be finished in 15 days, find the number of extra workers required.
Step-by-step explanation:
20 workers finish work in 21 days.
the necessary work effort is 20×21 = 420 workdays.
the same effort is needed even if the overall time is shorter.
x workers in 15 days.
x × 15 = 420
x = 420/15 = 28 workers.
so, 28-20 = 8 additional workers are needed to finish the work in 15 days.
Is x2 4x 4 a perfect square trinomial?
x² + 4x + 4, this is a perfect square trinomial, which is expressed as
(x + 2)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 4x + 4
= (x)² + 2(2x) + 4
= (x)² + 2(x)(2) + 2²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 2)²
= (x + 2) (x + 2)
so, this is a perfect square trinomial.
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483000 in standard form
Answer:
483000
Step-by-step explanation:
To write a linear expression in standard form, rearrange the terms in alphabetical order.
Answer:
48300000
We can write the above number as
4.83 x 10000000
=4.83 x 10 ^7
Which of the options below are the terms of the expression 5x² + 9x + 6? Choose all of the correct answers. 5x 9x 6 X x² 5 5x² 9
The terms of the expression are 5x², 9x and 6
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.
They are also known to be made up of arithmetic operation, such as;
DivisionAdditionParenthesesMultiplicationSubtractionBracket, etcIt is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.
They can be regrouped by the addition of their coefficients. Like terms are those that has the same variables to the same powers or coefficients.
The types are;
5x², 9x and 6
Thus, they are 5x², 9x and 6
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Find the measure of x.
14
X
48
x = [?]
Answer:
18.84
Step-by-step explanation:
x is the hypotenuse of the triangle.
For the 48° angle, 14 is the opposite leg.
The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine.
sin 48° = opp/hyp
sin 48° = 14/x
x × sin 48° = 14
x = 14/sin 48°
x = 18.84
A catering company is setting up tables for a big event that will host 764 people when they set up the tables they need 2 forks for each child and 5 forks for each adult the company ordered a total of 2992 forks set up a system of equations involving the number of adults,a and the number of children,c and solve to find out how many of each attended the event
Answer:
488 adults and 276 children
Step-by-step explanation:
So, we need two linear equations here to start, and we do have them.
Our first linear equation tells us how we get the number of forks:
2c + 5a = 2992
And the second tells us the number of people there:
c + a = 764
I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:
c = 764 - a
Then, we will substitute this into our first equation, giving us:
2(764 - a) + 5a = 2992
Then, we will open the parentheses, giving us:
1528 - 2a + 5a = 2992
Combining like terms and subtracting 1528 from both sides gives us:
3a = 1464
Dividing by 3:
a = 488
So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:
488 + c = 764
Minus 488 from both sides gives us:
c = 276
So, there were 276 children. In total, we had 488 adults and 276 children.
Hope this helped!
i need help with this question
The required slope of the linear equation is -3 which values shown in the table.
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The table is given in the question as follows:
x y
-4 -15
-2 9
0 3
2 -3
4 -9
As per the question, we take the given points are (0, 3) and (4, -9).
So we can substitute these values into the formula:
m = (-9 - 3) / (4 - 0)
m = -12 / 4
Apply the division operation, and we get
m = -3
Therefore, the required slope of the linear equation is -3.
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Any help is appreciated<3
A jewelry shop is offering a percent discount on the original price of a jade pendent. The original price of the pendant was $200.
Let d represent the percent discount, written as a decimal. Write an equation to find the discount price, y dollars, of the pendant.
An equation to find the discount price, y dollars, of the pendant is y=2d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The original price of the pendant was $200.
Let d represent the percent discount, written as a decimal.
The discount price, y dollars, of the pendant.
y=d% of 200
y=d/100 ×200
y=2d
Therefore, an equation to find the discount price, y dollars, of the pendant is y=2d.
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What is the length of a leg of a 45 45 90 right triangle if the hypotenuse measures 5 square root of 2?
If the leg of the triangle is equal to a, then:
The second leg is also equal to a.
the given hypotenuse is a√2.
The given area is equal to a²/2; and
The perimeter equals a (2 + √2).
Now, looks easy, but from where does it come? There are various of methods to prove that equation, the most popular of them are:
By using the Pythagorean theorem, we can do that.
As you know one leg length a, then you know the length of the other as well, as both of them are equal.
The given 45 45 90 triangle shows the remaining parameters. Now you know that:
hypotenuse length is - 9 in * √2 = 12.73 in.
area is - 9 in * 9 in / 2 = 40.5 in²; and
perimeter - 9 in + 9 in + 9 in * √2 = 30.73 in.
Find the hypotenuse from the Pythagorean theorem:
a² + b² = c² => a² + a² = c² so c = √(2a²) = a√2
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two cards are chosen at random from a deck of 52. what is the probability that both cards are numbers (2 through 10) totaling to 12
The probability is 0.3845.The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.Explanation:
2/52 * 10/52 = 20/52 = 0.3845.
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The triangle ACE, is a dilation image of triangle ABD. Point A is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation. The length of side AC is 15.
Answer:
Enlargment and 5/4
Step-by-step explanation:
A jar contains 7 red jelly beans, 2 black jelly beans and 6 green jelly beans. You draw ONE jelly bean. What is the probability of drawing a red bean? a. c. 1 b. d.
Answer:
7/15
Step-by-step explanation:
number of favorable outcomes (red jelly beans) = 7
number of total outcomes (total jelly beans) = 7 + 2 + 6 = 15
probability of red = number of favorable outcomes/number of total outcomes = 7/15
The probability of getting a red jelly bean is 7/15
Total number of jelly beans in the jar (sum of all the jelly beans): 7+6+2= 15
Total number of red jelly beans: 7
Therefore, the probability of getting a red jelly bean= number of red jelly beans/ total number of jelly beans
=7/15
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The quotient of 18 and the number is three what is the number
Answer:
Step-by-step explanation:
Divide: 18 ÷3=?
The answer is 6
what is 20% of 14000
Answer:
2800
Step-by-step explanation:
20% of 14,000 is 2800
Multiply both sides by 14,000, then divide the left side to get the result.
Answer:
2800
is what the calculator says
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
both Square and Rectangle
because all squares are rectangles, but not all rectangles are squares. Hope this helps. :)
Find a basis for the eigenspace corresponding to the eigenvalue. 2-6 Al La 2 = 11 9 A basis for the eigenspace corresponding to a = 11 is a (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Use a comma to separate answers as needed) Find a basis for the eigenspace corresponding to the eigenvalue of A given below. A= 3 02 0 4,2 = 2 2 -3 3 A basis for the eigenspace corresponding to a = 2 is O. (Use a comma to separate answers as needed.)
A basis for the eigenspace corresponding to a = 11 is (1, -2, 0) and a basis for the eigenspace corresponding to a = 2 is (0,1,1).
An eigenspace is the set of all vectors that are multiplied by a matrix and remain unchanged. In this case, the eigenspace is the set of all vectors that when multiplied by the matrix A will result in a vector with a scalar multiple of the eigenvalue. The eigenvalue is found by solving the characteristic equation, which is the determinant of the matrix minus the eigenvalue multiplied by the identity matrix.
For the matrix A, the eigenvalues are 11 and 2. The corresponding eigenspace for each eigenvalue is then found by solving the homogeneous system of equations. For a = 11, the solution to the system is (1, -2, 0) and for a = 2, the solution is (0,1,1). Both of these vectors form a basis for the corresponding eigenspaces.
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If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives
the largest percentage of their gross pay in employee benefits?
a. Employee A: gross pay $32,600, total job benefits $33,600
b. Employee B: gross pay $32,900, total job benefits $34,000
c. Employee C: gross pay $33,400, total job benefits $33,900
d. Employee D: gross pay $33,700, total job benefits $34,700
The employee who receives the largest percentage of their gross pay in employee benefits is Employee D.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviation "pct". For instance, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentage can be used to express part-to-whole relationships, such as "25% of the students in the class". It can also be used to compare two or more values, such as "the temperature rose by 3% over the course of the day". In some cases, percentage can be used to calculate a quantity from a given value, such as finding the percentage increase from one number to another.
This is because they have the highest total job benefits ($34,700) when compared to their gross pay ($33,700). This results in a percentage of 103.3%, which is the highest of the four employee options.
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Solve this problem
Step by step
The value of x in the shape we have here is given as 18.7 cm
How to solve for the value of xIn this question we are to find the value of x using the values that we already have in the shape.
The base of the diagram has its length as 40 cm.
The shape is made up of two right angled triangles.
since the top of the shape is 26 m, the triangles would be gotten by
40 - 26 = 14
14 / 2 = 7cm
each rectangular base is therefore 7 cm
we have to solve for the value of x using the Pythagorean theorem
hence we would have:
7² + x² = 20²
49 + x² = 400
x² = 400 - 49
x² = 351
x = 18.7 cm
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there can be more than one answer
The spring constant is 30 N/m and the stretch when the 420 N force is applied is 14 cm.
What is spring force?The force needed or applied to compress or extend a spring on any attached object is known as the spring force.
A spring exerts an equal and opposite force on an object when the object exerts a force on it. It always takes action to get mass back to where it should be for equilibrium.
Given that when 180 N force is applied the spring stretched by 6 cm. The spring stretch when the 420 N force is applied is calculated as,
First, calculate the spring constant,
F = kx
180 = k x 6
k = 30 N / m
Calculate the deformation,
x = F / k
x = 420 / 30
x = 14 cm
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Square root of 16b power four
Answer: 256b
Step-by-step explanation: So, first we need to find the square root of 16b.
That'd be 4b, because a square root is when a number can be divided by a number, such as 4 can go into 16 4 times, and like 5 can go into 25 5 times. So, we got 4b
So, 4 to the power of 4 (ignore the b right now) is the same as 4 x 4 x 4 x 4.
So simplified, that'd be 16 x 4 (64). So, 64 x 4 = 256.
So, I'd be 256b
Andy and Trevor share 40 sweets in a ratio 11: 9
How many more sweets does Andy receive than Trevor does?
Answer:
Step-by-step explanation:
no
Answer:
22:18
Step-by-step explanation:
In this case, firstly you have to add 11 and 9 together, which makes 20.
Then, 40 ( number of sweets ), divided by 20 gives us 2.
This means that every piece, or block, of our ratio will be 2.
Therefore, the last step is multiplying 11x2 and 9x2.
So, Andy has 22 sweets an Trevor has 18.
Q4 ABC is an isosceles triangle with AB=AC and AD is one of its altitudes. i) State the three pairs of equal pairs in ADB and ADC.
ii) Is ADB = ADC? Why or why not?
iii) Is B=C? Why or why not?
iv) Is BD=CD? Why or why not?
Answer:
d
Step-by-step explanation:
What is the value of x in the equation 2.5 6x 4 )= 10 4 1.5 0.5 x?
The value of x in this problem is 2.
Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.
Use the transposing method to isolate the variable x and then solve for it.
distribute brackets on both sides of the equation.
= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x
= 15x - 10 = 10 + 6 + 2x
collect terms in x to the left side and numeric values to the right side.
= 15x - 2x = 10 + 6 + 10
= 13x = 26
= x = 26/13 = 2
Therefore the final value of x in this equation will be 2.
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Please help quickly!
Use the figure below to answer questions 18-21
Answer:
Step-by-step explanation:
18. m∠1 = 104°
19. m∠2 = 79°
20. m∠3 = 65°
21. m∠5 = 73°
What is log and example?
Logs are a type of mathematical operation used to solve exponential equations.
Logs are written as log boxes, where b is the base. The base is the number that the logarithm is being calculated concerning. The x is the number that the logarithm is calculated. Logarithms allow us to convert multiplication and division problems into addition and subtraction.
For example, log2 (8) can be calculated by taking the logarithm of 2, which is 0.301029996, and then multiplying it by 8, which is 2.408239965. This means that log2 (8) is equal to 2.408239965.
Another example is log10 (100). This can be calculated by taking the logarithm of 10, which is 1 and then multiplying it by 100, which is 100.
This means that log10 (100) is equal to 100. Logs are an important tool in mathematics and are used in a variety of fields, such as chemistry, engineering, and economics.
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Please its due today
a) The domain and the range of the function are given as follows:
Domain: [-4,5).Range: [0,9].b) The zero of the function is given as follows: (3,0).
c) The behaviors are given by these following intervals:
Increasing: (-4,0) U (3,5).Decreasing: (0,3).Constant: DNE.d) The extremas are given as follows:
Relative minimum: (3,0).Relative maximum: (0,9).e) The function is neither even nor odd.
What are the features of the function?The domain of a function is the set that contains all the input values for the function, hence in the graph it is given by the values of x.
The range of a function is the set that contains all the output values for the function, hence in the graph it is given by the values of y.
The zeros are the points of the function at which it either crosses or touches the x-axis.
The function is increasing when the graph is moving up, and decreasing it the graph is moving down.
The extremas are given as follows:
Relative minimum: function changes from decreasing to increasing.Relative maximum: function changes from increasing to decreasing.The function is classified as even, odd or neither as follows:
Even: f(x) = f(-x) for all values of x.Odd: f(-x) = -f(x) for all values of x.Neither: none of the two above statements are true.More can be learned about functions at https://brainly.com/question/24808124
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