The statement that is true about the quadratic functions is:
g(x) > h(x) for x = -1.
Which statements are true for functions g(x) and g(x)?Here we have the two quadratic functions:
g(x) = x^2
h(x) = -x^2
Notice that h(x) = -g(x).
Also, g(x) is always positive or zero, while h(x) is always negative, but for x = 0 both have the same value.
g(0) = 0^2 = -0^2 = h(0)
Then the statement that is true is
g(x) > h(x) for x = -1.
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The Venice flagpole is 27 feet tall.
Myrna Loy's outstretched fingertip is 18 feet above the ground.
If a 24 foot long wire is stretched between the top of the flagpole and Myrna's fingertip, how far is Myrna's fingertip from the top of the flagpole?
Draw a diagram, then solve for the missing side. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
I probalby am not reading the question correctly, but it seems be be asking the distance between Myrna's fingertip (18 feet above the ground!) and the top of the 27' foot flagploe. We are not told where Myrna is standing, nor how she got her fingertip 18 feet high. Since we are asked for a diagram, I did the best I could, not knowing much about Myrna other than she must be tall. On her behalf, I assumed Myrna was directly under the flagpoe. As shown in the attached diagram, her fingertip is 9 feet below the top of the flagpole.
If the 24 foot wire is stretched all the way (i.e., it takes 24 feet to reach Myrna's fingertip), then she is not standing directly below the flagpole. But this isn't clear in the problem. In any event, if the question is how far she is from the very top of the flagpole from where she is standing, it would be the 24 foot lenght of the wire connecting her to the top of the flagpole. If the question just wants the vertical distance, then it is 9 feet.
If she is standing away from the flagpole, then a diagram would appear roughly as follows:
x
x s
x 27' s 24'
x s
x ----------z-------------- y
x y
x y 18'
x ----------z-------------- y
flagpole Myrna
The distance z is calculated using the Pythagorean Theorem in the top triangle. The left side is (27'-18') or 9'. The hypotenuse is 24'.
z^2 + 9^2 = 24^2
z = 22.2 feet.
you are flipping 100 coins, putting aside those that come up heads after each flip. how many flips do you expect to make before running out of coins to flip?
5050 flips expect to make before running out of coins .
Let's approach this problem using the concept of geometric distribution.
The probability of getting heads on any given coin flip is 1/2, assuming a fair coin.
So the probability of getting tails on a given flip is also 1/2.
The number of flips it takes to get the first head is a geometric distribution with a probability of success p = 1/2.
The expected number of flips until the first head appears is 1/p = 2 flips.
After the first head appears, there will be 99 coins left to flip.
The expected number of flips until the next head appears is still 2, since the probability of getting heads on any given flip is still 1/2.
So the expected number of flips until the second head appears (and the number of coins remaining drops to 98) is 2+1 = 3 flips.
Similarly, the expected number of flips until the third head appears (and the number of coins remaining drops to 97) is 2+1+1 = 4 flips.
We can generalize this pattern: after k heads have been obtained, the expected number of additional flips until the next head appears (and the number of coins remaining drops to 100-k) is k+1 flips.
Using this formula, we can calculate the expected number of flips to obtain all 100 heads:
E(number of flips) = (2 + 3 + 4 + ... + 101)
= (1 + 2 + 3 + ... + 100) + 100
= (100 x 101 / 2) + 100
= 5050
Therefore, we expect to make 5050 flips before running out of coins to flip and obtaining all 100 heads.
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write the set b=1/10 1/100 1/1000 in set builder form
The set builder form of the set b = {1/10, 1/00, 1/1000} is b = {x | x = 1/10ⁿ, where n is a positive integer}
In mathematics, set builder notation is a concise way of describing a set using a rule or a formula.
Let's explore how we can use set builder notation to write the set b={1/10, 1/100, 1/1000}.
To begin, we need to identify the common property that these elements share. In this case, we can observe that each element is a rational number with a power of ten as the denominator. So, we can write the set b as follows:
b = {x | x = 1/10ⁿ, where n is a positive integer}
In this notation, the vertical bar represents "such that" and separates the description of the element from the rule that defines the set. The letter x is a variable that represents any element that satisfies the rule. We use the power of ten as a common property to describe the set b.
In this set builder form, we can see that b is a set of elements that can be expressed as 1/10 to the power of a positive integer. We can also use set builder notation to define other sets with different properties, such as sets of even numbers or sets of prime numbers.
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$190 is invested in an account earning 7.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer:
Value of account after t years is
[tex]A = \boxed{190( 1.0178)^{4t}}[/tex]
Percentage of growth per year
CAGR = [tex]\boxed{7.31\%}[/tex]
Step-by-step explanation:
The generalized equation for the accrued value of an amount P(the principal) deposited at i% annual interest compounded n times a year for t years is
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
where r = i/100, the interest rate expressed as a decimal
Given P = $190
i = 7.1% ==> r = 7.1/100 = 0.071
Since the interest is compounded quarterly and there are 4 quarters in a year, the interest is compounded 4 times a year so n = 4
[tex]A = 190 \left(1 + \dfrac{0.071}{4}\right)^{4t}[/tex]
[tex]A = 190\left(1 + 0.01775\right)^{4t}}\\\\A = 190( 1.01775)^{4t}[/tex]\
Rounding the annual growth rate to 4 decimal places gives
[tex]A = P(1.0178)^{4t}[/tex]
In one year, the investment of $190 will grow to
[tex]A = 190(1.0178)^{4}[/tex]
[tex]A = $203.89[/tex]
Compound Annual Growth = = 203.89 - 190 = $13.89
Compound Annual Growth Rage(CAGR) = $13.89/$190 = 0.073105
As a percentage, CAGR Percent = 0.073105 x 100 = 7.3105% or rounded to nearest hundredth it would be 7.31%
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of center?
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.
The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.
For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.
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Please help me with this!! ( please answer thinking wuestion
1. In his newspaper, Peter Zenger published articles criticizing the Governor's use of arbitrary power
2. Because it was against the law to criticize the king or his appointees, the Attorney General accused Peter Zenger of committing" libel.
3. Hamilton believed Zenger was not guilty of this charge because in Zenger's newspaper articles the "truth is told
4. Hamilton felt that more than just Peter Zenger was on trial. He felt that the larger concept of American" liberty was at stake.
How to convey the informationHamilton and Morris agreed that the trial of Peter Zenger was important for American freedom and the defense of liberty.
As for the question about television and newspaper reporters, it is a matter of opinion. Some people believe that the freedom of the press is an important part of democracy, and that reporters should be able to criticize anyone in power, including the president. Others believe that criticism of the president should be limited to protect the dignity and stability of the office. In either case, it is important to strike a balance between free speech and responsible journalism.
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Katie is 1.62 m tall George is 3cm shorter than Katie how tall is George
consider the equation 4(10^-3x)=18, solve the equation for x. Express the solution as a logarithm in base-10.
The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
[tex]\rm 4 \times (10^{-3x})=18[/tex]
Simplify the equation, then we have
[tex]\begin{aligned} \rm 4 \times (10^{-3x}) &=18\\\\\rm (10^{-3x}) &=4.5 \end{aligned}[/tex]
Take a log with base 10 on both sides, then we have
- 3x log₁₀ 10 = log₁₀ 4.5
- 3x = 0.6532
x = -0.2177
The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.
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in nine bernoulli trials, what is the probability that there will be more than the expected number of failures?
The probability of having more than the expected number of failures (i.e., at least five failures) in a set of nine Bernoulli trials is 0.2461, assuming that the probability of failure is 0.5.
In the field of probability, it is essential to understand the expected number of successes or failures in a given set of trials. However, what happens when we observe more or fewer outcomes than expected? In this scenario, we need to calculate the probability of observing a specific number of failures in a set of Bernoulli trials.
Let's assume that the probability of failure is denoted by "p," and the probability of success is denoted by "q." Thus, the expected number of failures in nine Bernoulli trials is given by:
E(X) = np
where n is the number of trials, and p is the probability of failure. In this case, n = 9, and we need to determine the probability of having more than the expected number of failures. This means we are interested in finding the probability of observing at least five failures since the expected number of failures is given by:
E(X) = 9p
If we assume that the probability of failure is 0.5 (i.e., p = 0.5), then the expected number of failures is 4.5 (i.e., E(X) = 9 * 0.5 = 4.5). Therefore, we are interested in finding the probability of observing at least five failures in nine Bernoulli trials.
To calculate this probability, we need to use the binomial distribution formula, which is given by:
[tex]P(X = k) = (^n_k) \times p^k \times q^{n-k}[/tex]
where P(X = k) is the probability of observing k failures in n trials, (n choose k) is the binomial coefficient, which is calculated as n! / (k! (n-k)!), p is the probability of failure, q is the probability of success (i.e., q = 1 - p), and k is the number of failures we are interested in observing.
Using this formula, we can calculate the probability of observing at least five failures in nine Bernoulli trials as follows:
P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= (9 choose 5) x 0.5⁵ x 0.5⁴ + (9 choose 6) x 0.5⁶ x 0.5³ + (9 choose 7) x 0.5⁷ x 0.5² + (9 choose 8) x 0.5⁸ x 0.5¹ + (9 choose 9) x 0.5⁹ x 0.5⁰
= 0.2461
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Evaluate each expression using substitution and order of operations. Show your thinking.
(y + 2)² at y = -4
Answer:
(y+2)^2
= y^2 + 4y + 4
now plug in -4 in y's
=(-4)^2 + 4(-4) + 4
=8-16+4
=-4
An apple pie is cut into six equal slices. If the diameter of the pie is ten inches, what is the approximate arc length of one slice of pie?
A 1.67 in.
B 3.14 in.
C 5.24 in.
D 13.08 in.
The approximate arc length of one slice of apple pie, when the diameter of the pie is ten inches, is option (c) - 5.24 inches.
We know that the apple pie is cut into 6 equal slices,
therefore, Θ = 360/6 = 60° (for each slice of the apple pie)
then the diameter of the apple pie is, d = 10 inches
from the diameter we can find the radius, r = 10/2 inches = 5 inches
arc length = 0/360 × 2[tex]\pi[/tex]r
we put the values of r and [tex]\pi[/tex] into the equation, we get the following:
= 60/360 × [tex]2\pi[/tex] × 5
= 5.24 inches.
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Use the word bank to complete the statements below.
A reflection over the x-axis.
A vertical stretch by 11 units.
A translation left by 5 units.
A translation up 4 units.
What is reflection over graph?The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.
An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.
Here, f(x) = 1/x²
Now, reflect the graph over the x-axis to obtain the graph of:
f(x) = -1/x²
Now, stretch the graph vertically by 11 units to get the graph of:
f(x) = -11/x²
Again, translate the graph left by 5 units to obtain the graph of:
f(x) = - 11 / (x + 5)²
Now, translate the graph up by 4 units to obtain the graph of:
f(x) = 4 - {11 / (x + 5)²}
Hence,
A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.
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What algebraic expression could represent the average of 2x, 3 + x and 6x?
The algebraic expression in simplified form representing the average is 3x + 1.
To solve this question, one must know the formula of average. It is as follows -
Average = sum of the numbers / quantity of numbers
Now, we see that there are 3 expressions in the question. Hence, quantity of numbers will be 3.
Sum of the numbers = 2x + 3 + x + 6x
So, keep the values in formula to find the expression -
Average = 2x + 3 + x + 6x/ 3
Simplifying the expression to find average
Average = 9x + 3/3
Performing division on Right Hand Side of the equation
Average = 3x + 1.
Hence, required algebraic expression is 3x + 1.
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The prices and weights of three boxes of cereal are shown below.
Brand A: $1.99 for 12 ounces Brand B: $2.29 for 16 ounces Brand C: $2.99 for 18 ounces
If you choose among these three boxes, what is the lowest unit price, in dollars, you can pay? If necessary, round your answer to the nearest cent.
Answer:
Brand b
Step-by-step explanation:
brand a is 0.165 per ounce
brand b is 0.143 per ounce
brand c is 0.166 per ounce
Answer probability question PLSSSSS
Answer:a is 3:9 B is 6:9
Step-by-step explanation:
this is just for fun I already know the answer but I will give branly and a lot of points to who ever answers
2+2
Answer:
4
Step-by-step explanation:
Answer: 4
Step-by-step explanation: Because 1+1=2
2+2=4 therefore 2*2 also equal 4 and 2^2= 4
cover all material from the lessons but will hopefully remind you of key points. To be prepared,
you must study all packets from Unit 1.
A salesman tracks the number of cars he sells through the model c, where c(m) is number of cars sold
and m is the month for 0 ≤ m ≤ 24.
1. What does c(10) represent?
2. What does
c(16)-c(8)
16-8
represent? 3. What does
represent?
c(7)-c(6.999)
7-6.999
a. It should be noted that c(10) represents the number of cars sold in the 10th month.
b. c(16) - c(8) represents the number of cars sold in the 16th month minus the number of cars sold in the 8th month. This difference could represent the net change in the number of cars sold between those two months.
What is a function about?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. The process of evaluating a function is typically straightforward when we have the function in the form of a formula.
In this case, c(10) represents the number of cars sold in the 10th month.
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The human body produces about $4. 8\times10^6$4. 8×106 red blood cells in 4 times 10 to the negative 2 power$4\times10^{-2}$4×10−2 minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form
The total number of red blood cells produced by human body in each minute is given by [ 1.2 × 10^8 ] red blood cells
Number of red blood cells produced by human body = 4. 8 × 10^6
Time taken by human body to produce 4. 8 × 10^6 red blood cells
= 4×10^(−2) minute
Number of red blood cells produced by human body in one minute are :
4 × 10^(−2) minute = 4. 8 × 10^6 red blood cells
⇒ 1 minute = [ 4. 8 × 10^6 / 4 × 10^(−2) ] red blood cells
⇒ 1 minute = [ 1.2 × 10^( 6 - (−2) ) ] red blood cells
⇒ 1 minute = [ 1.2 × 10^( 6 + 2) ) ] red blood cells
⇒ 1 minute = [ 1.2 × 10^8 ] red blood cells
Therefore, total number of red blood cells produced by human body in one minute is equal to [ 1.2 × 10^8 ] red blood cells.
The above question is incomplete, the complete question is:
The human body produces about4. 8×10^6 red blood cells in 4×10^(−2) minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form.
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7. 3 You are presented with three coins. You are told that two of them are fair, meaning thatif flipped, they will return heads or tails with a 0. 5 probability. You are also told that one isweighted, and will return heads 0. 8 of the time and tails 0. 2. You pick one coin arbitrarilyand flip it; it returns heads. Calculate the probability that the coin you are holding is theweighted one, given that it returned heads on one flip
The probability of the coin being the weighted one given that it returned heads is 0.8.
P(Weighted | Heads) = ( P(Heads | Weighted) * P(Weighted) ) / P(Heads)
= ( 0.8 * 0.5 ) / 0.5
= 0.8
The probability of the coin being the weighted one given that it returned heads can be calculated using Baye's Theorem. This theorem states that the probability of an event given a condition is equal to the probability of the condition given the event multiplied by the probability of the event divided by the probability of the condition. In this case, the event is the coin being weighted, the condition is the coin returning heads. Therefore, the probability of the coin being the weighted one given that it returned heads is equal to the probability of the coin returning heads given that it is weighted multiplied by the probability of the coin being weighted divided by the probability of the coin returning heads. The probability of the coin returning heads given that it is weighted is 0.8, the probability of the coin being weighted is 0.5, and the probability of the coin returning heads is 0.5. Thus, the probability of the coin being the weighted one given that it returned heads is 0.8.
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Find the area of the polygon in square units.
The area of the polygon is 7.5 square units
How to determine the area of the polygonNote that the polygon given in the diagram takes the shape of a kite.
The properties of a kite are given as;
It two pairs of adjacent equal sidesIt has one pair of opposite angles that are equalThe diagonals are equalThe shorter diagonal forms two isosceles trianglesThe longer diagonal forms two equal trianglesThe diagonals are perpendicular to each otherThe formula for area of a kite is;
Area = pq/2
Area = 3(5)/2
Area = 15/2
Divide the values
Area = 7.5 square units.
Thus, the value is 7.5 square units
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A procedure for using sample data to find the estimated regression equation is
a. point estimation. b. interval estimation.
c. the least squares method. d. extrapolation.
Option C. the least squares method is a procedure for using sample data to find the estimated regression equation.
The procedure for using sample data to find the estimated regression equation is called the least squares method. This method involves finding the line that minimizes the sum of the squared vertical distances between the observed data points and the line. The estimated regression equation is used to predict the value of the dependent variable based on the value of the independent variable. This method is commonly used in regression analysis to model the relationship between two variables. It is a useful tool for making predictions and understanding the relationship between variables.
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if $m$ is a real number and $x^2 mx 4$ has two distinct real roots, then what are the possible values of $m$? express your answer in interval notation.
The m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:
m ∈ (-∞, -4) ∪ (4, ∞).
The quadratic formula tells us that the quadratic equation's roots
[tex]x^2 + mx + 4 = 0[/tex]
are provided by:
[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]
The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:
Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.
Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.
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A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 36° and AB = 8.6. Calculate the length of AC rounded to 3 SF.
Answer:
AC ≈ 6.25
Step-by-step explanation:
using the tangent ratio in the right triangle
tan36° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × tan36° = AC , then
AC ≈ 6.25 ( to 3 SF )
I NEED HELP ON THIS ASAP!!!!
In mathematics, a line is a set of points that extend indefinitely in two directions.
How to explain the linePoints on the line: These are points that lie exactly on the line. They are equidistant from the two endpoints of the line and are considered to be part of the line itself.
Points above the line: Points that are vertically above the line are referred to as points above the line. These points are located higher than the line and have a greater y-coordinate than any point on the line.
Points below the line: Points that are vertically below the line are referred to as points below the line. These points are located lower than the line and have a smaller y-coordinate than any point on the line.
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random sample of 92 sophomores are asked whether they plan to attend Homecoming. Of these, 51 sophomores said they will attend. What is the margin of error at 90% confidence and its interpretation?
0.102; 90% of the time we will capture the true proportion of sophomores who will attend Homecoming within 0.102 of the population proportion
0.085; 90% of the time we will capture the true proportion of sophomores who will attend Homecoming within 0.085 of the population proportion
0.102; we are 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.102 of the sample proportion
0.085; we are 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion
The margin of error at 90% confidence and its interpretation is;
0.085; we are 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion
How to find the margin of error?The margin of error is defined as a term used in statistics to find the confidence interval. It is denoted by E.
The formula for margin of error is;
E = z(√(p(1 - p)/n)
The parameters are given as;
Sample size; n = 92
sample of success; x = 51
Sample proportion; p = 51/92 = 0.554
z at 90% CL = 1.645
Thus;
E = 1.645(√(0.554(1 - 0.554)/92)
E = 0.085
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Given that 4ax² + 9x + c is always negative, what conditions must apply to the constants a and c?
Answer:
Step-by-step explanation:
According to question
[tex]4ax^{2} +9x+c < 0[/tex]
This means that the coefficient of the highest degree term
([tex]4ax^{2}[/tex]) must be positive
And the constant term (c) must be negative
So, the according to condition
4a must be positive,
which means a must be positive
And, c must be negative
[tex]a > 0\\c < 0[/tex]
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Write a quadratic equation with -1 and 5 as its roots
A quadratic equation with -1 and 5 as its roots is x^2 - 4x - 5 = 0 by multiplying the terms.
The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Derive factor from the roots
x = -1 and x = 5
x + 1 = 0 and x - 5 = 0
Now, (x+1)(x-5) = 0
x(x - 5) + 1(x - 5) = 0
x^2 - 5x + x - 5 = 0
x^2 - 4x - 5 = 0
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At the beginning of a snowstorm, Kaj had 7 inches of snow on her lawn. The snow
then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was
melting, how much snow would Kaj have on her lawn 3 hours after the snow began to
fall? How much snow would Kaj have on her lawn after t hours of snow falling?
After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
After 3 hours of snow falling, Kaj would have:
7 + 0.5(3) = 8.5 inches of snow on her lawn.
To find how much snow Kaj would have on her lawn after t hours of snow falling, we can use the following formula:
S = 7 + 0.5t
where S is the amount of snow on Kaj's lawn in inches and t is the time in hours since the beginning of the snowstorm.
For example, if we wanted to find how much snow Kaj would have on her lawn after 5 hours of snow falling, we could substitute t = 5 into the formula:
S = 7 + 0.5(5) = 9.5
Therefore, After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.
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Use the Distributive Property to solve each equation.
a. −1/2(b−6)= 5
b. 0.4(x−0.45)= 9.2
c. −4(p−212)=44
please help
The required answers are
a) b = -4
b) x = 23.45
c) p = 201
Distributive Property:The distributive property implies that multiplying a number by the sum of two or more addends yields the same result as dividing the multiplier, multiplying each addend individually, and combining the products . It can be given as,
a (b+c) = d
[tex](a*b) + (a*c) = d[/tex]
Now in the given question,
a) −1/2(b−6)= 5
by distributive property , we have
[tex](\frac{-1}{2} *b)-(\frac{-1}{2}*6 )=5\\\frac{-1}{2}b+3=5\\\frac{-1}{2}b=2\\b=-4[/tex]
b) 0.4(x−0.45)= 9.2
by distributive property , we have
0.4x - 0.4(0.45) =9.2
0.4x -0.18 = 9.2
0.4x = 9.38
x = 23.45
c) −4(p−212)=44
by distributive property , we have
-4p +4 (212) = 44
-4p + 848 =44
-4p = 44 - 848
-4p = -804
p = 201
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How to solve this question ??
The number in question is the magic sum of the square. The outcome is the same as if you multiply the three integers in each column together and then add the three products: 8, times 3, 4, 1, 5, 6, 7, and 2 equals 225. This quantity is known as the magic square product.
What is an integers?The term "integer" refers to any number that is not zero, a positive natural number, or a negative integer denoted by a minus sign. Because they are diametrically opposed to their positive counterparts, negative integers are additive.
When representing a group of numbers in mathematical notation, the blackboard bold mathbb Z or boldface Z are frequently used. The word "integer" is pronounced "IN-tuh-jer" and refers to a whole number that can be positive, negative, or zero.
A few examples of integers are -5, 1, 5, 8, 97, and 3,043. Non-integer numbers include the figures -1.43, 1 3/4, and 3.14.
The integers are a collection of all whole numbers and their antipodes. Decimal points and fractions are not included in the set of integers. The numbers 2, 5, 0, 12, 244, 15, and 8 are examples.
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