The scale factor of dilation of the 10 cm by 10 cm picture to produce the 4 m by 4 m copy on the wall indicates that the dimension of the copy of the 1 cm by 1 cm box on the wall is 40 cm.
What is a scale factor?A scale factor is the factor or number of times by which the size of a pre-image is reduced or increased.
Possible parts of the question includes;
Dimensions of the picture = 10 cm × 10 cm
The dimensions of the wall = 4 m × 4 m
The dimensions of each box in the picture = 1 cm × 1 cm
The dimensions of each box on the wall are found as follows;
The linear scale factor of the picture to the copy of the picture on the wall is; 10 cm ≡ 4 m
Therefore; 1 cm ≡ (4/10) m = 0.4 m
1 centimeters is to 0.4 meters son the wall
10 cm on the picture is equivalent to 4 meters on the wall
Therefore;
(10 cm)/10 = 1 cm on the picture is equivalent to (4 m)/10 = 0.4 m on the wall
1 meters = 100 centimeters
0.4 meters = 0.4 × 100 centimeters = 40 centimetersThe dimension of the box on the wall is therefore; 40 cm × 40 cm
The best correct option is; 40 cm
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Solve.
7. x + 1/4 = 2
Answer:
x=7
Step-by-step explanation:
(x+1)/4=2
x+1=2*4
x+1=8
x=7
A hotel packed breakfast for each of the three guests. Each breakfast should have consisted of threeTypes of rolls, one each of nut, cheese and fruit rolls. The preparer wrapped each of the nine rollsand once wrapped, the rolls were indistinguishable from one another. She then randomly put threerolls in a bag for each of the guests. If the probability that each guest got one roll of each type ism/n where m and n are relatively prime integers, find the value of (m+n).
The probability that each guest got one roll of each type is 3/1, which is a fraction with a numerator of 3 and a denominator of 1. Since the numerator and denominator are relatively prime integers, the value of m + n is 3
The equation for the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers.
We can expand this equation to
m/n
= 3/1.
Since the numerator and denominator are relatively prime integers, we can solve for m + n by multiplying both sides of the equation by 1.
Multiplying both sides of the equation by 1 gives us
m + n = 3.
Therefore, the value of
m + n is 3.
Let m = numerator and n = denominator in the probability of m/n.
Given that each guest got one roll of each type, the probability is m/n.
The numerator and denominator are relatively prime integers, so m and n have no common factors.
Therefore,
m + n = 3.
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1 The temperature in Moscow is – 8C. The temperature falls by 8degrees. Write down the new temperat
The new temperature of Moscow is - 16°C dropped - 8°C from - 8°C.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The temperature in Moscow is - 8°C.
Now, The temperature falls by 8°C.
Therefore the resultant temperature can be obtained by subtracting the temperature drop from the initial temperature of Moscow which is,
= - 8°C - 8°C.
= - 16°C.
So, The new temperature is - 16°C.
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A person deposits Rs 10,000/- in a bank which offers an annual compounded interest of 9%. What is the amount he can receive after 3 years?
The amount received after 3 years is ₹12950.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Given that, principal = ₹10,000, rate of interest =9% and time period = 3 years.
Now, amount =10000(1+9/100)³
= 10000(1.09)³
= 10000×1.295
= ₹12950
Therefore, the amount is ₹12950.
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At the market, almonds cost $0.51 per ounce. How much does a bag of almonds cost if it weighs 1.6 ounces?
Answer:
A bag of almonds that weighs 1.6 ounces will cost $0.51 x 1.6 = $<<0.51*1.6=0.816>>0.816.
Step-by-step explanation:
Lesson 23: Using Quadratic Expressions in
Vertex Form to Solve Problems
Cool Down: Looking for The Greatest or the Least
1. Without graphing, find the vertex of the graph of a quadratic function defined by
1²-14x-60. Show your reasoning.
2. Does the y-coordinate of the vertex correspond to a maximum or a minimum value
of the function? Explain how you know.
The vertex of the quadratic expression will be at (7, -109). The parabola opens upward, then the minimum value of the expression will be - 109.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The quadratic expression is given below.
⇒ x² - 14x - 60
Convert the expression into a vertex form. Then we have
⇒ x² - 14x - 60
⇒ x² - 14x + 49 - 49 - 60
⇒ (x - 7)² - 109
The vertex of the quadratic expression will be at (7, -109). The parabola opens upward, then the minimum value of the expression will be - 109.
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Take away 3/5 from 7/10?
Answer:
To subtract or add a fraction you must first find a common deniminator between the two.
you can use 10 as a common denomonator in this case.
3 x 2 = 6
5 x 2 = 10
your new fraction to replace 3/5 is 6/10
Now, your equation would be 7/10 - 6/10 = 1/10
Your answer is 1/10
What is the solution to this Equation?
Answer: C, 85
Step-by-step explanation:
Hopefully, that is a fourth root :)
Raise the entire equation to the fourth power.
x-4 = 3^4
x - 4 = 81
x = 85
Option C matches the answer
Which of the following inequalities matches the graph?
x>4
x<4
y>4
v<4
The answer choice which correctly represent the inequality that matches the given graph as required is; y < 4.
Which inequality among the answer choices matches the graph?As evident in the task content; the given graph includes a shaded region whose boundary line is parallel to the horizontal axis and has a y-intercept; 4.
On this note, since the given border line is a broken line, it follows that the inequality sign is; > or <.
Ultimately, since the region below the line is shaded, the required inequality is; y < 4.
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A scale drawing of a square has a side length of 5 centimeters. The drawing has a scale of 1 cm : 5 ft. Find the actual perimeter and area of the square.
area =729 feet square and perimeter = 108 feet
Given the side of a square is 9 cm.
The scale is given as :
1 cm = 3 feet Since 1 cm represents 3 feet.
Therefore, 9 cm will represent = 9 x 3 feet= 27 feet
So the side of the square is 27 feet.Therefore, its area = Side x side= 27 x 27 = 729 feet square
And the perimeter = 4 x side= 4 x 27= 108 feet
What is perimeter?In the conventional system of measurement, an inch is a unit of length. Either in or " can be used to represent length in inches. For instance, 16 in or 16" can be used to write 5 inches. In both the British imperial and American customary systems of measurement, the inch serves as a unit of length. It is equivalent to 1/12 of a foot or 1/36 of a yard. a unit of length that is equivalent to 1/12 foot, or 2.54 centimeters, in length. In the conventional system of measurement, an inch is a unit of length. Either in or " can be used to represent length in inches.To learn more about perimeter refer to:
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Simplify:
2√20-2√5
A.)√5-√5
B.)2
C.)2√5
D.)4√4-√5
Answer:
To simplify the expression 2√20 - 2√5, you can start by applying the rule that the square root of a product is the product of the square roots of the factors. This means that you can rewrite √(20) as √(4*5) = 2√(5).
Applying this rule, the expression simplifies to:
2√(5) - 2√(5) = 2√(5) - 2√(5) = 0
Therefore, the simplified expression is equal to 2√(5).
Step-by-step explanation:
Help
This picture shows two vectors and with solid grey arrows. There is a third vector shown with a dashed arrow. Its head is near the head of 7. p The third vector is: Select one: A. PI q B. p-q OC. None of the other answers. D. p+q E. d
Correct option is C, the resultant vector will be [tex]\vec{p} + \vec{q}[/tex].
What does a basic math vector mean?A vector is something that possesses both magnitude and direction. A vector is a directed line segment in geometry, with an arrow pointing in the direction and a length equal to the vector's magnitude.
A quantity or phenomenon known as a vector has two distinct properties: magnitude and direction. The phrase also specifies the mathematical or geometrical representation of such a quantity.
Examples of vectors in nature include velocities, moments of inertia, forces, electromagnetic fields, and weight.
Vectors are typically employed in air and sea navigation.
Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
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Y=-3 Y=Ax2+4x-4 In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?
A) -4
B) -2
C) 2
D) 4
For constant A to be -4 (option 1) the system of equations have exactly one real solution.
NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?
We have given, y=-3
y= Ax^2+4x-4
Therefore, -3= Ax^2+4x-4
or, Ax^2+4x-1=0
For second order equation of ax^2+bx+c=0 have a solution for
x= [-b± (√b^2-4ac)]/2a] [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]
For single solution b^2-4ac=0
here, Ax^2+4x-1=0
4^2 - 4a(-1)=0
16+4a=0
a= -(16)/4
a= -4
option A is correct .
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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.
B) -2
The given system of equations can be written as:
Y = A*x^2 + 4*x - 4
We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:
x = [-b +/- sqrt(b^2-4ac)]/2a
where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.
Substituting these values into the equation, we get:
x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A
Simplifying this, we get:
x = [-4 +/- sqrt(16 + 16A)]/2A
For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.
This is only true when A is equal to -2. Therefore, the correct answer is B) -2.
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Find the smallest positive integer k such that, for every positive integer n, 6n+k is relatively prime to each of 6n+3, 6n+2, and 6n+1.
Answer:
Use Mathpapa to find your answer.
Step-by-step explanation:
It's a good, and powerful program.
Use the segment to complete the
statements.
The value of x is ___
The length of in inches is ___
The length of ec in inches is ___
On solving the provided question, we can say that in the line, The value of x is 5; the length of in inches is 5; the length of ec in inches is 15
what is a line?A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line.
here,
The value of x is 5
The length of in inches is 5
The length of ec in inches is 15
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Graph the equation below by plotting the
y-intercept and a second point on the
line. When you click Done, your line will
appear.
y = 3x - 5
Answer:
See the graph below
Step-by-step explanation:
What is the slope of the line in the equation y = -4x + 3?
(no image)
Answer:
-4 is the slope
Step-by-step explanation:
y= mx + b
m being the slope
Hope this helps!
Answer: m= -4
Step-by-step explanation:
y=mx+b
b is your y-intercept
mx is your slope
the equation of y = -4x + 3 would be -4x
21. Higher Order Thinking The flags of all
5 Nordic countries are displayed.
What fraction describes how many more
of the flags displayed are 2-color flags the
are 3-color flags?
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
There are 3 2 colored flags and 2 3 colored flags.
2 colored flags to total flags is 3/5
Dominic says that the product of 827 and 53 is 43,511. Is his answer
correct? Explain.
No, Dominic's answer is incorrect.
To find the product of 827 and 53, you can use the standard multiplication algorithm that you would use for decimal numbers.
First, you need to multiply the rightmost digit of 53, which is 3, by 827. This gives you 2481.
Then, you need to multiply the next digit of 53, which is 5, by 827 and add this result to the previous one. This gives you 43,811.
Therefore, the product of 827 and 53 is 43,811, not 43,511 as Dominic has stated. Dominic's answer is incorrect because he has made an error in the calculation.
The following table gives you the distribution of marks secured by some students in anexamination. 0-20 21-30 31-40 41-50 51-60 61-70 71-80 no of students: 42 38 120 84 48 36 32 Find (i) Median marks (ii) the percentage of failures, if the minimum for a pass is 35 marks. (Ans. 40.5 and 30.5)
Is (1, 1) a solution to this system of equations?
6x + 14y = 20
8x + y = 6.
yes
no
No, this is not the solution for the following system of equation
What is system of equation?
When two or more equations are solved simultaneously, they are referred to be a system of equations. The objective is to identify the values of the variables that satisfy each of the equations in the system. These equations frequently have many variables.
Here is an illustration of a set of equations:
x + y = 7
x - y = 1
To determine whether a given point (x, y) is a solution to a system of equations, we need to substitute the values of x and y into the equations of the system and see whether the equations are satisfied.
In this case, we want to check if (1, 1) is a solution to the system of equations:
6x + 14y = 20
8x + y = 6
We substitute the given x and y values into the system of equations:
6(1) + 14(1) = 20
8(1) + 1 = 9
And see if the two equations are true
6 + 14 = 20 is true
8 + 1 = 6 is false
So (1, 1) is not a solution to the system of equations.
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Given: Lines 1 and 2 are parallel. Line 3 is a transversal.
Which statement justifies that ∠A ≅ ∠C:
A: If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent.
B: If 2 parallel lines are cut by a transversal, then the alternate interior angles are
congruent.
C: If 2 alternate interior angles are congruent, then the lines that have been cut by a
transversal are parallel.
D: If 2 corresponding angles are congruent, then the lines that have been cut by a
transversal are parallel.
A: If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:The measures of an exterior angle are 21,60°, and an interior angle is 360° in the given regular polygon with 14 sides.
Step-by-step explanation:
There are 16 city buses. There are 806 people waiting to get on a bus. How many people will not fit on a bus?
A
12 people
B
10 people
C
6 people
D
3 people
solve for x3(x-2)+4=28
Answer: here’s the answer!
Step-by-step explanation: hope this helps!
Answer:
x=10
Step-by-step explanation:
3(x-2)+4=28
3x-6+4=28
3x-2=28
3x=30
x=10
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line represented by the graph is -3
How to determine the slope of the lineFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings (when the lines representing the rise and the run are drawn)
Length of rise = -9
Length of run = 3
The slope of the line is then calculated as
Slope = Length of rise/Length of run
Substitute the known values in the above equation, so, we have the following representation
Slope = -9/3
Evaluate the quotient
Slope = -3
Hence, the line has a slope of -3
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11. Write the equation of the line with a slope of 2 that passes through the points (-2,-7) and
(5,7).
y-7=2x+5
y=2x
y=2x+3
y=2x-3
What do you think about given set of ordered pairs?
{ (-2, 1), (-1, 0 ) , ( 1, 0), (2, 0 ) }
Responses
A-It is a function.
B-It is a relation but not a function.
Note that the given set of ordered pairs are an example of a mathematical function. (Option A)
What is an ordered pair?An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. By situating a point on the Cartesian plane, it enhances visual comprehension. The numeric values of an ordered pair might be integers or fractions.
A function is a collection of ordered pairs in which each input (or "x" value) corresponds to exactly one output (or "y" value). In this provided set of ordered pairs: (-2, 1), (-1, 0), (1, 0), (2, 0), there is only one matching value of y for each value of x.
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Find all x-intercepts and y-intercepts of the graph of the function.
f(x)=3x³-12x²-15x
Answer:
To find the x-intercepts and y-intercepts of a function, we need to find the values of x and y at which the function crosses the x-axis or y-axis.
X-intercepts:
The x-intercepts occur when y = 0, so we can set f(x) = 0 and solve for x:
3x³-12x²-15x = 0
This is a cubic equation, we can use factoring, synthetic division or use a numerical method like the Newton-Raphson method to solve for x.
Y-intercepts:
The y-intercepts occur when x = 0, so we can substitute x = 0 into the function to find the y-intercept:
f(0) = 3(0)³ - 12(0)² - 15(0) = 0
So the y-intercept of the graph is at the point (0,0)
In summary, the x-intercepts are the solutions of the equation 3x³-12x²-15x = 0 and the y-intercept is (0,0)
Please note that, if the equation has complex roots, the graph will not cross the x-axis and hence it will not have any real x-intercepts.
Step-by-step explanation:
Which of the following did you include in your response? Check all of the boxes that apply. Use the distributive property to multiply the factors on the right side of the equation. Simplify the product by combining like terms. Show that the right side of the equation can be written exactly the same as the left side. Show that the right side of the equation simplifies to a cubed minus b cubed.
You can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²) based on the following responses:
A. Use the distributive property to multiply the factors on the right side of the equation.
B. Simplify the product by combining like terms.
C. Show that the right side of the equation can be written exactly the same as the left side.
D. Show that the right side of the equation simplifies to a cubed minus b cubed.
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
a³ – b³ = (a - b)(a² + ab + b²)
a³ – b³ = a(a² + ab + b²) - b(a² + ab + b²)
Next, we would combine like terms:
a³ – b³ = a³ + a²b + ab² - a²b - ab² - b³
a³ - b³ = a³ - b³.
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Complete Question:
Explain how you can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²)
Which of the following did you include in your response? Check all of the boxes that apply.
Use the distributive property to multiply the factors on the right side of the equation.
Simplify the product by combining like terms.
Show that the right side of the equation can be written exactly the same as the left side.
Show that the right side of the equation simplifies to a cubed minus b cubed.
