For what values of x does 25^x = 5^x^2-3?
The values of x that satisfy the given equation are -1 and 3
What is an indical equation?From the question, we are to determine the values of x that satisfy the given equation
The given equation is
25^x = 5^x^2-3
The can be written as
[tex]25^{x} =5^{x^{2} -3}[/tex]
Expressing 25 in index form, we get
[tex]5^{2x} =5^{x^{2}-3 }[/tex]
Now, equate the powers (since the bases are equal)
[tex]2x =x^{2}-3[/tex]
Then, we have that
[tex]x^{2} -2x-3 =0[/tex]
Solve quadratically
Using the factorization method, we get
[tex]x^{2} -2x-3 =0[/tex]
[tex]x^{2} -3x+x-3 =0[/tex]
[tex]x(x-3)+1(x-3)=0[/tex]
[tex](x+1)(x-3) =0[/tex]
∴ x+1 = 0 OR x-3 = 0
x = -1 OR x = 3
Hence, the values of x that satisfy the given equation are -1 and 3.
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Find distance between parallel lines given equations in 3d
The numbers on two consecutively numbered gym lockers have a sum of 129129. what are the locker numbers?
The area of a circle is found with the formula a = , where represents 3.14. if a tile artist is placing tiles in a circular mosaic pattern and the area of the circle is 658 square feet, what is the approximate radius of the circle in feet?
Answer:
14
Step-by-step explanation:
Area = 3.14πr^2
We know that the area of the circle is 658. Divide 658 by 3.14 which equals 209.5 ( rounded to the nearest whole number is 210). The square root of 210 is 14.4 and rounding to the nearest whole number is 14.
A box has a rectangular base with a length of 3x + 2 and width of 2x - 2, and the base has a perimeter of 60 centimeters. If the height of the box is x, what is the volume of the box?
The volume of the box is determined by finding the value of x from the perimeter equation, substituting it back into the expressions for length and width, and finally multiplying the dimensions with the height. Calculating these steps, the volume of the box is 1200 cm³.
Explanation:To find the volume of a box, we multiply its length, width, and height. The student has provided the length as 3x + 2, the width as 2x - 2, and the height as x. We also know the perimeter of the base is 60 centimeters.
First, we calculate the perimeter of the base, which is 2(length + width). Hence, we set up the equation: 2(3x + 2 + 2x - 2) = 60. Simplifying this, we get 2(5x) = 60, therefore x = 6 cm.
Second, we substitute x into the expressions for length and width to get the actual dimensions of the box base: length 3(6) + 2 = 20 cm, and width 2(6) - 2 = 10 cm.
Finally, we calculate the volume of the box as length × width × height = 20 cm × 10 cm × 6 cm = 1200 cm³.
Not sure how to do this. (I'm aware this is wrong lol)
Between what 2 integers does √89 fall?
A.9 and 10
B.10 and 11
C.11 and 12
D.12 and 13
Math problem : suppose you cut a sheet of papper into fourths and throw away three of the fourths. you cut the reminding fourths into fourths you repeat the process , each time cutting the paper into fourths and throwing away three of the fourths. after the sixth repetition what fraction of the original sheet of paper id left?
The three interior angle measures of this triangle are x = °, y = °, and z = °.
Answer:
30-70-80
Step-by-step explanation:
Select the coordinates of two points that are on the line x = 5.
(5, 0) and (0, 5)
(5, 0) and (5, −2)
(5, 0) and (0, 2)
(0, 5) and (0, 2)
The line x=5 is the vertical line consisting of all points with x-coordinate equal to 5 (see attached graph).
A. Point (0,5) has first coordinate 0 (not 5).
C. Point (0,2) has first coordinate 0 (not 5).
D. Points (0,5) and (0,2) have first coordinates 0 (not 5).
B. Only in this option both points have first coordinates 5.
Answer: correct choice is B
Divide 7/24 by 34/48 and reduce the quotient to the lowest fraction
The volume of a cone is 1004.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.)
64
32
8
4
Math : powers , help me !!!
Two lines intersect to form a linear pair with equal measures. One angle has the measure 3x° and the other angle has the measure (8y − 70)°. Find the values of x and y.
Answer:
Substitute by equation 1 in equation 2:
3x+3x = 180
6x = 180
x = 30
Substitute with the value of x in equation 1 to get y as follows:
3x = 8y-70
3(30) + 70 = 8y
160 = 8y
y = 20
Levain bakery, on west 74th street in new york city, is trying to determine the number of loaves of raisin bread to make each day. over the past few months the store has baked 50 loaves each day and has sold out with probability 0.80. suppose the owner continues this practice and 30 days are selected at random. fill in the blank. (give your answer to four decimal places.)
From the given information, the sample size is 30 days and the probability is 0.80.
Here, it can be observed that the number of trials is fixed and the probability of success is 0.80. So, apply binomial distribution. The number of trials is fixed and the probability of success is 0.80. So, apply binomial distribution.
The mean of the binomial distribution is obtained below:
Mean = np = 30 * 0.8 = 24
The expected number of days on which all 50 loaves will be sold is 24.
The mean value obtained by multiply the sample size (n) and the probability of success (p). That is, the expected number of days on which all 50 loaves will be sold is 24.
The expected number of days on which all 50 loaves will be sold is 24.
Ashley runs 6 miles in 49 minutes. how many miles does she run per minute?
It is now between 10:00 and 11:00. six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago what is the exact time now
The problem is solved by calculating the relative speed of the minute and hour hands of the clock and their current angular position. The current time when addressed the problem is approximately 10:26.
Explanation:The problem presents an instance of math calculation with clock hands. Here we'll use the fact that a full rotation of a clock’s hand indicates 360 degrees. In 60 minutes, the minute hand makes a full rotation, moving at a speed of 360/60 = 6 degrees per minute. In 12 hours, the hour hand makes a full rotation, moving at a speed of 360/(12*60) = 0.5 degrees per minute.
Three minutes ago, the hour hand was 3 * 0.5 = 1.5 degrees behind its current position. Six minutes later from now, the minute hand will be 6 * 6 = 36 degrees forward its current position. As per the conditions of the problem, the minute hand will be exactly opposite to the position held by the hour hand three minutes ago in six minutes from now. The opposite position in terms of the clock involves an angle of 180 degrees.
Therefore, the difference between the positions of the minute and hour hands right now = 180 degrees + 1.5 degrees - 36 degrees = 145.5 degrees. As the minute hand moves faster, the speed of the minute hand relative to the hour hand = 6 degrees - 0.5 degrees = 5.5 degrees per minute. Hence, the time required for the minute hand to create an angle of 145.5 degrees from the hour hand = 145.5 / 5.5 ≈ 26.45 minutes.
Therefore, the time now in HH:MM format is 10:26 (approximately), as the time was in the hour of 10.
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Write a function g in terms of f so that the statement is true.
The graph of g is a reflection in the y-axis of the graph of f
g(x)=
The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
Explanation:The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
To reflect a point across the y-axis, we change the sign of the x-coordinate. So, to reflect the graph of f(x) across the y-axis, we need to change the sign of f(x). This can be achieved by multiplying f(x) by -1, giving us g(x) = -f(x).
For example, if f(x) = 2x+3, then g(x) = -(2x+3) = -2x-3.
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The function g(x) that represents a reflection in the y-axis is g(x) = -f(x).
Explanation:The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
To reflect a graph in the y-axis, we replace each x-coordinate with its opposite (negative value) while keeping the y-coordinate unchanged. In this case, since g is the reflection of f in the y-axis, the function g(x) will have the same y-values as f(x), but the x-values will be their negatives.
For example, if f(x) = 2x + 3, then g(x) = -f(x) would be g(x) = -2x - 3, where the graph of g(x) is the reflection of f(x) across the y-axis.
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Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?
which of the following is a true statement? A.all states have a progressive state tax B.state income tax is an optional deduction C. certainly states have a flat state tax D. most states have no state income tax
What is the expression using summation notation of 0.4(1/2+1/2.4+1/2.8+1/3.2+1/3.6)?
The given expression, 0.4 times the sum of reciprocals in an arithmetic sequence, is expressed using summation notation. Calculating the numerical value yields approximately 0.5244.
Breaking down the expression and writing it using summation notation:
The given expression is: 0.4 (1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6)
To express it in summation notation, we need to identify the pattern in the sequence.
The terms are reciprocals of an arithmetic sequence, where each term is obtained by adding a constant difference (0.4) to the previous term.
The nth term of the sequence can be expressed as: 2 + 0.4(n-1)
The expression in summation notation is: ∑ (from n = 1 to 5) of 1/(2 + 0.4(n-1))
Calculating the values and finding the sum:
For n = 1: 1/(2 + 0.4(1-1)) = 1/2
For n = 2: 1/(2 + 0.4(2-1)) = 1/2.4
Similarly, for n = 3, 4, and 5, we get 1/2.8, 1/3.2, and 1/3.6, respectively.
Summing these values, we get: Sum = 1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6
Multiplying by 0.4 (as in the original expression), we have: 0.4 * (1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6)
Calculating the numerical value:
0.4 * (1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6) ≈ 0.5244
Therefore, the final numerical value of the expression is approximately 0.5244.
Simplify the expression (20-14)^2 divided by 12
A)1
B)3
C)17
D)0.5
Answer:
The correct option is B) 3.
Step-by-step explanation:
Consider the provided expression.
(20-14)^2 divided by 12
The above statement can be written as:
[tex]\frac{(20-14)^2}{12}[/tex]
[tex]\frac{(6)^2}{12}[/tex]
[tex]\frac{6\times 6}{12}[/tex]
[tex]\frac{36}{12}[/tex]
3 times 12 is 36,
[tex]3[/tex]
Hence, the simplified form of the provided expression is 3.
Therefore, the correct option is B) 3.
What is the slope of a line perpendicular to line q?
Find the x -intercept and the y -intercept. Then use them to graph the line of 6x+2y=-12
A rectangular persian carpet has a perimeter of 176 inches. the length of the carpet is 20 inches more than the width. what are the dimensions of the carpet?
The dimension of the carpet are 54 inches and 34 inches.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given,
A rectangular Persians carpet has a perimeter of 176 inches.
Now,
The perimeter of a rectangle is;
P =2W + 2L
In this case;
⇒ 176= 2W + 2L
Also, the 2nd sentence says;
⇒ L = W + 20
We can substitute this value of length in the perimeter formula as;
176 = 2W + 2(W+20)
176 = 2W+ 2W + 40
176 = 4W + 40
136 = 4W
34 = W
W = 34
Since, L = W +20
L = 34 + 20
= 54
Thus, The dimensions are 54 inches and 34 inches.
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The dimensions of the carpet are 54 inches in length and 34 inches in width. This was determined by setting up and solving the perimeter equation for a rectangle, after which we calculated the length by adding 20 to the width.
To determine the dimensions of a rectangular Persian carpet with a perimeter of 176 inches where the length is 20 inches more than the width, first, let's let the width be represented by w inches. The length will then be w + 20 inches. The perimeter of a rectangle is calculated by adding together twice the width and twice the length (P = 2w + 2l).
The formula with the given values will look like this:
176 = 2w + 2(w + 20)
Simplifying this equation gives us the width and subsequently the length:
176 = 2w + 2w + 40
176 = 4w + 40
136 = 4w
w = 34
So, the width of the carpet is 34 inches. To find the length, we add 20 inches to the width:
Length = w + 20 = 34 + 20 = 54 inches
Therefore, the dimensions of the carpet are 54 inches in length and 34 inches in width.
You pay $38.50 for a sweater that is marked 30% off the regular price. what is the regular price of the sweater? how much did you save by buying it on sale?
Write an equation for the line that is parallel to the given line and that passes through the given point.
y equals five halves x minus 10; the point negative 6, negative 29
A. y equals five halves x plus one hundred thirty three halves
B. y equals five halves x minus 14
C. y equals two fifths x minus 14
D. y equals negative two fives x plus 14
Answer:
The correct option is B.
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
The given equation is
[tex]y=\frac{5}{2}x-10[/tex]
It means the slope of the line is 5/2 and y-intercept is -10.
The slope of two parallel lines is same. So, the slope of required line is 5/2.
The equation of required line is
[tex]y=\frac{5}{2}x+b[/tex]
It is given that the line passes through the point (-6,-29).
[tex](-29)=\frac{5}{2}(-6)+b[/tex]
[tex]-29=-15+b[/tex]
[tex]-29+15=+b[/tex]
[tex]-14=b[/tex]
The y-intercept of required line is -14. So the equation of required line is
[tex]y=\frac{5}{2}x-14[/tex]
Therefore the correct option is B.
Answer:
the answer is B. y equals five halves x minus 14
Step-by-step explanation:
hope it helps
In a mixture of concrete, there are fourfour lb of cement mix for each pound of gravel. if the mixture contains a total of 110110 lb of these two ingredients, how many pounds of gravel are there?
Nadine is constructing a line perpendicular to KE←→ . She has constructed the arcs as shown. What is the next step in her construction? Use a straight edge to draw a line through D and M. Use a straight edge to draw a line through M and E. Use a straight edge to draw a line through M and K. The image shows a horizontal line with points K, D, and E from left to right. Point D looks halfway between points K and E. An arc is shown at point K turning inwards towards point D. An arc is shown at point E turning inwards towards point D. Above point D is point M. Two arcs go through point M. One arc faces southwest towards point K and one points southeast towards point E.
How does finding the square root of a number compare to finidng the cubic root of a number?
Final answer:
Square rooting and cube rooting are processes to find a number that, when raised to the second or third power respectively, equals the original number. Square roots are related to squares, and cube roots are related to cubes; both functions are essential in solving various mathematical problems, including equilibrium and Pythagorean Theorem problems.
Explanation:
Finding the square root of a number is the process of determining a number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 squared (5²) is 25. This can be expressed using exponents as x¹⁄₂ = √x.
On the other hand, finding the cube root of a number involves determining a number which, when multiplied by itself twice (or cubed), results in the original number. For instance, the cube root of 27 is 3, since 3 cubed (3³) equals 27. The formula for a simple equilibrium problem that involves cubic roots is a³ = M₁ × P², where you would then find the cube root of the result to solve for 'a'.
Both operations are inverse functions: square rooting is the inverse of squaring, and cube rooting is the inverse of cubing. When dealing with equilibrium problems or Pythagorean Theorem applications, it's important to know how to perform these operations, often requiring a calculator. Make sure you are comfortable with your calculator's functions for these operations, or seek assistance from your instructor if needed.