Although part of your question is missing, you might be referring to this full question: Which of the following options is an equivalent function to f(x) = 2(5)^2x? choices:
f(x) = 50^x
f(x) = 100^x
f(x) = 2(25)^x
f(x) = 4(25)^x
The equivalent function too expression is f(x)= 2(25)ˣ. Thus option c is correct.
The expression of function f(x) given, f(x)=2(5)²ˣ.
Functions are said to be equal if they have same domain or codomain such that f(x) = g(x). Thus, the two functions are equal functions.
∴ The function after solving expression is,
f(x)= 2×(5²)ˣ
f(x)= 2×(25)ˣ
Hence, the correct equivalent function is f(x)= 2(25)ˣ.
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The freezing point of seawater is −2 °C. The freezing point of nitric acid is −42 °C.
A photo of frozen seawater is shown.
How much greater is the freezing point of seawater than the freezing point of nitric acid?
The difference between the freezing point of seawater and the freezing point of nitric acid is 40 °C.
As per the question, we can write
The freezing point of seawater = −2 °C.
The freezing point of nitric acid = −42 °C.
We were asked to calculate the difference between the freezing point of seawater and the freezing point of nitric acid. We can find the difference between the freezing point of seawater and the freezing point of nitric acid by following the steps mentioned below;
The difference between the freezing point of seawater and the freezing point of nitric acid = Freezing point of Seawater - Freezing point of nitric acid
The difference between the freezing point of seawater and the freezing point of nitric acid = -2 - (-42) = 40 °C.
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A model of a rectangular stove top with four circular burners is shown. The side lengths of the stove top and the diameters of the burners are labeled.Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?A)108 in.2B)492 in.2C)420 in.2D)528 in.2
Explanation
to find the area of the stove that does not include the area of the burnes ( yellow area), we can subtract the area of the 4 circles from the area of the full rectangle
so
Step 1
[tex]\begin{gathered} \text{Area}=\text{rectangle-}4\text{ circles} \\ Area=(length\cdot width)-4(\pi\text{ }\frac{diameter^2}{4}) \\ A\text{rea}=(length\cdot width)-(\pi\text{ }\cdot diameter^2) \end{gathered}[/tex]
then, Let
for circle:
diameter= 6 in
for rectangle
length= 24 in
width= 22 in
Step 2
replace,
[tex]undefined[/tex]what is the answer of that
40° is the value of the angle ∠QPR.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.So, PQ ⊥ PS then, ∠QPS = 90°.
According to the given figure: ∠QPR + ∠RPS = ∠QPS
Then,
7x - 9 + 4x + 22 = 9011x + 13 = 9011x = 90 - 1311x = 77x = 7So, ∠QPR = 7x - 9°
Substitute x = 7 as:
7(7) - 9°49 - 9°40°Therefore, 40° is the value of the angle ∠QPR.
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Long division worked out 19 divided by 6,927
As per the long division, the value of 19 divided by 6,927 is 0.002742
Long division:
Long division is the mathematical method for dividing large numbers into multiple smaller groups or parts. The number which we divide into small groups is called the dividend, the number by which we divide is called the divisor.
Given,
Here we have to divide the number 19 by 6927.
When we divide the number, we have to following the following steps,
1) Set up the problem with long division bracket. Put dividend inside bracket and divisor on outside left.
2) 6927 goes into 19000 (2-times). Put a 2 in the next place of quotient and multiply 6927 by 2 to get 13854. Subtract 13854 from 19000 to get remainder (19000-13854=5146).
3) Now, bring down 0 from the dividend, to make 51460
4) 6927 goes into 51460 (7-times). Put a 7 in the next place of quotient and multiply 6927 by 7 to get 48489. Subtract 48489 from 51460 to get remainder (51460-48489=2971).
5) Now, bring down 0 from the dividend, to make 29710
6) 6927 goes into 29710 (4-times). Put a 4 in the next place of quotient and multiply 6927 by 4 to get 27708. Subtract 27708 from 29710 to get remainder (29710-27708=2002).
7) Now, bring down 0 from the dividend, to make 20020
8) 6927 goes into 20020 (2-times). Put a 2 in the next place of quotient and multiply 6927 by 2 to get 13854. Subtract 13854 from 20020 to get remainder (20020-13854=6166).
This process is continued so we have to take only up to these one.
Then this can be displayed in the following figure.
Question: Divide the number 19 by 6,927 using the long division method.
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Find 3/4 divided by 2/3 then draw a picture and write an explanation describing how to get the answer.
The outcome of the quotient between the two fractions 3/4 and 2/3 is 9/8
How to find the quotient between the two fractions?So let's define two fractions as:
a/b and c/d.
The quotient between the fractions a/b and c/d can be written as:
(a/b)÷(c/d).
Now, the quotient is equal to the product with the inverse, so we can rewrite this as:
(a/b)÷(c/d) = (a/b)*(d/c)
Now, in this case, we want to find 3/4 divided by 2/3, this will be:
(3/4)÷(2/3) = (3/4)*(3/2) = 9/8
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If the graph is that of a function, what are the intercepts of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A.The intercept(s) is/are nothing.(Type an ordered pair. Use a comma to separate answers as needed.)B.The graph is not that of a function.
To know if a graph represents a function, we have to use the vertical line test, which consists in drawing a vertical across the curve.
If the vertical line intercepts twice the curve, then it's not a function.
Therefore, the graph is not a function.Then, the graph has no function symmetry because the graph is not that of a function.
Therefore, the answer to part 4 is E.which expression would be easier to simplify if you use the associative property to change the grouping A: [-14+(-26)]+67B: (2/5+3/5) +7/3C: (43 + 60) + 40D: (50+50)+63
The associative property let us associate different terms or factors in order to solve some expression.
We have to find the expression in which this property is more useful.
The only expression where the associative may be helpful is C, as we can associate this way:
(43 + 60) + 40 = 43 + (60 + 40) = 43 + 100 = 143
In the other expression there is no advantage in applying this property.
Answer: C
Write an equation of the line passing through the point A(6,-1) that is perpendicular to the line y=-2x+8
Answer:
[tex]y+1=\frac{1}{2}(x-6)[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.
Substituting into point-slope form, the equation is
[tex]y+1=\frac{1}{2}(x-6)[/tex]
Mark's football team has scored about 24 points each game. They played 12 games this season.
What is the best estimate for the total number of points they scored in the season?
Ο Α. 150
B. 250
OC. 20
OD. 360
Answer:
250
Step-by-step explanation:
Scientists are drilling a hole in the ocean floor to learn more about the Earth's history. Currently, the hole is in the shape of a cylinder whose volume is approximately 3500 cubic feet and whose height is 4.8miles. Find the radius of the hole to the nearest hundredth of a foot. (Hint: Make sure the same units of measurement are used.)
The radius of the hole to the nearest hundredth of a foot will be 0.20 feet.
The problem we are dealing with here is related to volume, which is referred to as may be a degree of involved three-dimensional space. It is regularly measured numerically utilizing SI-inferred units (such as the cubic meter and liter) or by different majestic units (such as the quart, gallon, and cubic inch) and the volume formula we are referring to is of the cylinder which is,
Volume = πr²h
Where r is the radius of the cylinder, π is the constant which is equal to 3.14 and h is the height of the cylinder.
From the information given to us, the volume of the hole ( cylindrical in this case ) is 3500 cubic feet and the height is 4.8 miles
So First we Converting the 4.8 miles to feet,
Since we know 1 mile = 5280 feet
therefore, 4.8 miles = 4.7 × 5280 = 25344 feet
Now putting the desired in the formula,
=>3500 = 3.14 × r² × 25344
=> 79580.16r² = 3500
=>r² = 3500/79580.16
=>r²= 0.04398
=>r = √0.04398
= 0.2097 feet
= 0.20 feet
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What is f^-1(-7) plus f(-7)? I need help answering this question
Answer:
13
Step-by-step explanation:
You want the sum of f^-1(-7) and f(-7) given the function definition in the table.
Inverse functionThe inverse function f^-1(x) consists of ordered pairs that are the reverse of the ordered pairs (x, f(x)). That is ...
(x, f^-1(x)) ≡ (f(x), x)
Another way to describe f^-1(x) is "the value of z that gives f(z) = x". This means f^-1(-7) is the value of x that gives f(x) = -7. That x-value is 6:
f^-1(-7) = 6 . . . . . from the 4th column of the table
Function valueWe can read the function value directly from the table:
f(-7) = 7 . . . . . . the first column of the table
SumThen the sum of interest is ...
f^(-1)(-7) +f(-7) = (6) +(7)
f^(-1)(-7) +f(-7) = 13
__
Additional comment
The inverse function ordered pairs are ...
(x, f^-1(x)) = {(7, -7), (12, 11), (8, -13), (-7, 6), (13, 5)}
Your family is buying macaroni salad and potato salad for the family reunion.
The macaroni salad costs $2.00 per pound and the potato salad costs $3.00 per
pound. Write an equation that represents the cost of the salad your family buys
for the reunion if they spend $20.
Graph your equation in standard form. What are two different possible combinations of each salad that your family can buy for $20? Use the graph to find your answers.
If the amount of money is even, then the item that costs an odd number of money has to be bought an even number of times. Some possible combinations could be 2 lb potato salad and 7 lb Mac salad, or 4 lb potato salad and and 4 lb mac salad, or 6 lb potato salad and 1 lb mac salad.
There are 4 triangles and 8 squares. What is the simplest ratio of triangles to squares?
Answer:
1:2
Step-by-step explanation:
For every triangle there are two squares.
On a coordinate plane, point A is located (-2,2) and point B is located at (6,-1). Determine the coordinates of the point that is 7/8 of the distance from a to b
The coordinates of the point that at 7/8 from a to b are (5, -5/8)
How to determine the coordinate of the point on the line segment?On the segment, we have the following endpoints
A = (-2, 2)
B = (6, -1)
Also, we have the line ratio to be
Ratio, m : n = 7/8
Express the ratio as a ratio
So, we have
m : n = 7 : 8 - 7
Evaluate the difference
So, we have
m : n = 7 : 1
The coordinate of the point at the given distance is then calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)
Evaluate the products
So, we have
Point = 1/8 * (42 -2, -7 + 2)
Evaluate the sum and the difference
So, we have
Point = 1/8 * (40, -5)
Evaluate the products
So, we have
Point = (5, -5/8)
Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)
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PLEASE HELP ME I NEED 4 ANSWERS !!!!!!!!!! a) Fill in the gaps to factorise the expression below.
3x² + 16x + 5 = (3x + −)(x + −)
b) Use your answer to part a) to solve 3x² + 16x + 5 = 0
The roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.
As per the question statement, we are supposed to fill the gaps to factorize the quadratic equation given :
3x² + 16x + 5 = (3x + _)(x + _)
We need to solve the expression for finding out its factors.
y = 3x² + 16x + 5
y = 3x² + 15x + x + 5
y = 3x(x + 5) + 1(x + 5)
y = (3x + 1)(x + 5)
Therefore, the roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.
Quadratic equation: Any equation where there is just one term that squares the unknown and none that raises it to a higher power.Roots: Roots of any quadratic equation / expression is the value of the variable at which the complete value of the expression becomes zero (0). Number of roots = highest degree.To learn more about Quadratic equation, click on the link given below:
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Find X and Y
The triangles are congruent
As The triangles are congruent the value of y = 1 and x = 4
What is a triangle ?The basic polygonal shape of a triangle has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol. It has three connected vertices. Triangles can be divided into a variety of categories according on their sides and angles.
AS the triangles are congruent
15x-8y = 52.....(i)
6x +14y +142=180
6x +14y = 38
3x +7y =19 ....(ii)
x=[tex]\frac{19-17y}{3}[/tex]
15([tex]\frac{19-17y}{3}[/tex])-8y = 52
5(19-17y)-8y=52
95-85y-8y =52
93y =93
y = 1
x =4
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Find the slope between the following points (8,-4) and (2, -4)
Let:
[tex]\begin{gathered} (x1,y1)=(8,-4) \\ (x2,y2)=(2,-4) \end{gathered}[/tex]We can find the slope m, using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-4-(-4)}{2-8}=\frac{0}{-6}=0[/tex]Answer:
0
The area of the parallelogram is 24 square miles.find base and height
The base of the parallelogram is 3
The height of the parallelogram is 8
How to calculate the base and height of the parallelogram ?Let the base be represented as (x+2)
Let the height be represented as (x-2)
The area of the parallelogram is 24
The first step is to get two numbers that can be multiplied together to get 24
= 3 × 8
The two numbers are 3 and 8
Hence the base is 3 and the height is 8
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Exploring Sample Space
In the given sample spaces, which has the largest sample space?
M-{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A {10, 20, 30, 40, 50, 60, 70, 80, 90}
T{20, 25, 30, 35, 40, 45, 50, 55, 60}
H-{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}
????
Find the absolute change and the relative change in the following case.
The number of daily newspapers in a country decreased from 2271 in 1900 to 1218 in 2010.
The absolute change is _____
(Simplify your answer. Type an integer or a decimal.)
Answer:
-868
Step-by-step explanation:
-Absolute change is simply defined as the number by which a change has occurred.
-We therefore determine the difference between the two years by subtracting the new value from the old or reference value
You roll a six-sided die twice. What is the probability of rolling a 2 and then a 6?A.1 / 3B.1/6C.1/36D.1/12
Answer:
C. 1/36
Explanation:
The probability of rolling a 2 in a six-sided die is 1/6 because there are 6 possible outcomes and 1 of them is 2. In the same way, the probability of rolling a 6 is also 1/6 because there are 6 possible outcomes and 1 of them is 6.
Then, the probability of rolling a 2 and then a 6 can be calculated as:
[tex]P=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}[/tex]Because they are independent events and each one has a probability of 1/6.
Therefore, the answer is:
C. 1/36
What is the least common dominator of 5/12, 7/16
Answer:
the least common denometer for 5/12, 7/16 would be 48.
Step-by-step explanation:
Question
Solve the formula C = πd for л.
Two or more expressions with an Equal sign is called as Equation.π= C/d for equation C = πd
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is C = πd
c equal to pi times of d
We need to solve it for π
To solve for π we have to separate π from d. To make this We have to divide both sides by d.
So C/d= π
Hence π= C/d for equation C = πd
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a) The length of a rectangular hall is three times the breadth of the hall. What is the length if the breadth is b metres?
b) What is the length of the hall if the breadth is 12 m?
a. The length is (3b) meters
b. length of hall is 36m.
We have given,
a. Breadth of the rectangle = b meters,
Since, length of a rectangular hall is 3 times the breadth of the hall,
⇒ Length = 3 × Breadth
⇒ Length = 3b
Hence, the length of the rectangle is (3 b) meters.
b. if the breadth is 12 m
Then, the length of the hall = [tex]3\times 12[/tex]
= 36m.
What is length?Length is a measure of distance. In the International System of Quantities, length is a quantity that has a measured distance. In most measurement systems, a base unit of length is chosen from which all other units are derived. In the International System of Units, the basic unit of length is the meter. Length generally refers to the widest dimension of a fixed object. However, this does not always happen and may depend on the location of the object.
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The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is 3.91. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is .24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at confidence. Round up to the next whole number.
a. The desired margin of error is .11 The appropriate sample size is
.
b. The desired margin of error is .07 . The appropriate sample size is
.
c. The desired margin of error is .04. The appropriate sample size is
Answer:
3
Step-by-step explanation:
1 = 1
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.
The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.
[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.
2² × 2³ = (2×3)² = 6², using the power of a product.
[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.
The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.
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A bag of flour has a mass of 4.5 kilograms. How many grams are in 4.5 kilograms?
The first thing we have to know is that 1 kilogram is equal to 1000 grams
[tex]\begin{gathered} 1\operatorname{kg}\to1000gr \\ \frac{1000gr}{1\operatorname{kg}} \end{gathered}[/tex]if we have 5.4 kilograms
[tex]\begin{gathered} 4.5\operatorname{kg}\cdot\frac{1000gr}{1\operatorname{kg}}=(4.5)(1000gr) \\ \end{gathered}[/tex][tex]4.5kg=4500gr[/tex]Given m/5 = 91° and m/2 = (8x + 1)°, what is the value of x ?
X =
Helpppp
In the picture there is a parallel line with the intersection line. ∠5=91° and ∠2=(8x+1)°and x value is 11.
Given that,
In the picture there is a parallel line with the intersection line.
We have to find the x value.
Given ∠5=91° and ∠2=(8x+1)°
We know that if there are 2 parallel line and 1 line is intersecting to the parallel line then the corresponding angles are equal.
∠1=∠5
So, ∠1=91°
Now,
We can write as ∠1+∠2=180° because the ∠1 and ∠2 are on 1 line.
91+8x+1=180
8x+92=180
8x=180-92
8x=88
x=88/8
x=11
Therefore, x value is 11.
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which graph represents the inequality 2.5 greater than the product of -0.5 and a number?
The graph of the inequaity expression is added as an attachment
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to plot the graph of the inequaity expression?The mathematical statement is given as
"2.5 greater than the product of -0.5 and a number"
Product means times
So, we have the following representation
"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 greater than -0.5 * a number
Let the number be x
So, we have
"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 greater than -0.5x
Greater than is represented by >
So, we have
"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 > -0.5x
Next, we plot the graph of the inequality expression
See attachment for the graph of the inequality expression
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Find the value of x so that f(x) =7
HELP ASAP
The value of x, so f(x)=7 is 5.
According to the graph, we have a linear function and linear functions have the same slope for all value of x, we can determine the value of f(x) for x=7 by the means of the equation for the line:
[tex]\frac{y_{b}-y_{a} }{x_{b}-x_{a} }[/tex] = [tex]\frac{y_{c}-y_{a} }{x_{c}-x_{a} }[/tex] ....................(1)
Where:
[tex](x_{a},y_{a} )[/tex] = (2,0) and [tex](x_{b},y_{b} )[/tex] = (5,7) are the Known points.
[tex](x_{c},y_{c} )[/tex] is the Expected point.
The value of [tex]y_{c}[/tex] = 7
Then the value of [tex]x_{c}[/tex] is,
[tex]x_{c}=x_{a} +\frac{ y_{c}-y_{a} }{y_{b}-y_{a} } *(x_{b} - x_{a} )[/tex]
= 2+ [(7-0) / (7-0)] * (5-2)
= 2 + (5-2)
= 2+3
= 5
Therefore, the value of x, so f(x)=7 is 5.
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