The function that describes the equation S = 10S = P x P - 2P + 2 is
\(f(P) = (P^2 - 2P + 2)/9.\)
The given equation S = 10S = P x P - 2P + 2 can be simplified by combining like terms and dividing both sides by 9:
\(9S = P^2 - 2P + 2\)
We can rearrange this equation to solve for S in terms of P:
\(f(P) = (P^2 - 2P + 2)/9\)
Therefore, the function that describes this equation is:
\(f(P) = (P^2 - 2P + 2)/9\)
This function takes an input value of P and outputs the corresponding value of S that satisfies the original equation. The domain of this function is all real numbers since any value of P can be plugged into the equation. However, the range of this function is limited to non-negative values, since S represents a sum of numbers and cannot be negative.
In summary, the function that describes the equation
S = 10S = P x P - 2P + 2 is
\(f(P) = (P^2 - 2P + 2)/9.\)
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arabella graphed the following systems equations. she says that (0.5,2.5) is the solution.
what is one way you can use substitution to see if Arabella is correct
substitute __ for ___
Answer:
4x y
Step-by-step explanation:
Express -23 in the form bi where b is a real number TIME SENSITIVE
Answer:
A
Step-by-step explanation:
i stands for square root of negative 1. If you multiple i and square root of 23 you will end up with the original
help please. I'm stuck on this question
Will mark brainliest
Answer: The number is 2
Step-by-step explanation: Suzie says that \(\frac{1}{2}\), which is half of a whole, is equal to only \(\frac{1}{4}\) of the unknown number. This means that to find the value of the unknown number, you need to multiply \(\frac{1}{2}\) by 4 so that it equals to \(\frac{4}{4}\) of the mystery number.
Simply put, multiply \(\frac{1}{2}\) by 4. Then reduce for the answer, and this gives us these equations.
\(x=4(\frac{1}{2} )\)
\(x=\frac{4}{2}\)
\(x=2\)
Hope that this helps!
when operating under ifr with a vfr-on-top clearance, what altitude should be maintained?
When operating under Instrument Flight Rules (IFR) with a Visual Flight Rules (VFR) on-top clearance, the altitude to be maintained depends on the specific clearance and regulations in place.
Generally, when flying VFR-on-top, the pilot is authorized to operate in VFR conditions above a layer of clouds or other obscuring phenomena. In terms of altitude, the pilot is expected to maintain a cruising altitude appropriate for the direction of flight and comply with the relevant airspace regulations. This typically involves flying at the appropriate altitude for the specific airspace class, as defined by the Federal Aviation Regulations (FARs) or the applicable regulatory authority. It's important for pilots to review and understand the specific requirements and altitude restrictions outlined in their VFR-on-top clearance, as well as any additional instructions provided by air traffic control.
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Diane is participating in a 5-day cross-country biking challenge. She bikes for 47, 46, 61, and 50 miles on the first 4 days. How many miles does she need to bike on the last day so that her average (mean) is 53 miles per day
Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs S2, and a piece of fudge costs $3. This system of inequalities models the scenario: 2x + 3y = 15 x+y²3 Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points) Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points) Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points) PLEASE PLEASE HELP ME I REALLY NEED THIS DONE RIGHT ILL GIVE BRAINLEST
The set of inequalities represented by x + y ≥ 3 is the Michael wants to buy enough cupcakes and fudge with his $15 to feed at least three siblings.
what is inequality ?A interaction between two expressions like values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a link among two values that do not equal. Egality and inequality are different. The not equal symbol is typically used to indicate that two values are also not equal (). Different inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. Negative values are split or added on either side. Switch between the left and right.
given
Michael wants to spend his $15 on enough cupcakes and fudge to feed at least three siblings.
A cupcake costs $2 but a slice of fudge costs $3.
With this inequality approach, the following scenario is simulated:
2x + 3y ≤ 15
x + y ≥ 3
The set of inequalities represented by x + y ≥ 3 is the Michael wants to buy enough cupcakes and fudge with his $15 to feed at least three siblings.
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Please help asapppp
a. The area of the mirror = 6,644.24 cm²; Circumference of the mirror = 288.88 cm
b. The area would be needed; c. circumference would be needed.
How to Find the Circumference and Area of a Circle?To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius
To find the area of a circle, you can use the formula A = πr², where A is the area, π (pi) =3.14, and r is the radius of the circle.
a. Area of the mirror = πr² = 3.14 * 46²
= 6,644.24 cm²
Circumference of the mirror = πr² = 2 * 3.14 * 46
= 288.88 cm
b. To find the amount of glass needed, the measure that would be used is the area.
c. To find the amount of wire needed, the measure that would be used is the circumference.
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a. The area of the mirror = 6,644.24 cm²; Circumference of the mirror = 288.88 cm
b. The area would be needed; c. circumference would be needed.
How to Find the Circumference and Area of a Circle?To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius
To find the area of a circle, you can use the formula A = πr², where A is the area, π (pi) =3.14, and r is the radius of the circle.
a. Area of the mirror = πr² = 3.14 * 46²
= 6,644.24 cm²
Circumference of the mirror = πr² = 2 * 3.14 * 46
= 288.88 cm
b. To find the amount of glass needed, the measure that would be used is the area.
c. To find the amount of wire needed, the measure that would be used is the circumference.
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Please help me on this!
Answer:
C
Step-by-step explanation:
Linear functions will be greater than exponential functions at first- however, exponential equations will gradually surpass the linear equation.
cubic feet. The box has a length of
(x + 8) feet, a width of x feet, and a height of (x − 2) feet. Find the dimensions of the box.
Answer:
Step-by-step explanation:
To find the dimensions of the box, we need to solve for the value of x in the expressions given for its length, width, and height.
The volume of a box is given by multiplying its length, width, and height, so we can write:
V = (x+8) * x * (x-2)
Expanding the expression, we get:
V = (x^3 + 6x^2 - 16x)
We know that the volume of the box is measured in cubic feet, so we can assume that V is a positive value. Therefore, we can set V equal to some positive number, such as 1000 or 2000, and solve for x using algebraic techniques such as factoring or the quadratic formula.
For example, if we set V = 1000, we can write:
1000 = x^3 + 6x^2 - 16x
Simplifying and rearranging the terms, we get:
x^3 + 6x^2 - 16x - 1000 = 0
Using a graphing calculator or other mathematical software, we can find that the real solution to this equation is approximately x = 10.5.
Therefore, the dimensions of the box are:
- Length: x+8 = 18.5 feet
- Width: x = 10.5 feet
- Height: x-2 = 8.5 feet
miss austin gives her class 6 sets of data and asks them to identify which data set can most accurately be summarized by the mean. what topic is she covering?
Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.
This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.
Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.
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suppose thatx1,x2,...,xnandy1,y2,...,ynare independent random samples from pop-ulations with meansμ1andμ2and variancesσ21andσ22,respectively.showthatx−yis aconsistent estimator ofμ1−μ2
We have shown that X¯ − Y¯ is a consistent estimator of µ1 − µ2.
To show that X¯ − Y¯ is a consistent estimator of µ1 − µ2, we need to demonstrate that it converges in probability to µ1 − µ2 as the sample size n approaches infinity.
First, let's define X¯ and Y¯:
X¯ = (X1 + X2 + ... + Xn) / n
Y¯ = (Y1 + Y2 + ... + Yn) / n
Now, let's consider the difference X¯ − Y¯:
X¯ − Y¯ = (X1 + X2 + ... + Xn) / n - (Y1 + Y2 + ... + Yn) / n
Using algebraic manipulation, we can rewrite this as:
X¯ − Y¯ = [(X1 - Y1) + (X2 - Y2) + ... + (Xn - Yn)] / n
Since X1, X2, ..., Xn and Y1, Y2, ..., Yn are independent random samples, the individual differences (X1 - Y1), (X2 - Y2), ..., (Xn - Yn) are also independent.
Now, let's calculate the expected value and variance of X¯ − Y¯:
E(X¯ − Y¯) = E[(X1 - Y1) + (X2 - Y2) + ... + (Xn - Yn)] / n
= [E(X1 - Y1) + E(X2 - Y2) + ... + E(Xn - Yn)] / n
= [µ1 - µ2 + µ1 - µ2 + ... + µ1 - µ2] / n
= n(µ1 - µ2) / n
= µ1 - µ2
Var(X¯ − Y¯) = \(Var[(X1 - Y1) + (X2 - Y2) + ... + (Xn - Yn)] / n^2\)
=\([Var(X1 - Y1) + Var(X2 - Y2) + ... + Var(Xn - Yn)] / n^2\)
\(= [σ1^2 + σ2^2 + ... + σ1^2 + σ2^2] / n^2\)
= \((nσ1^2 + nσ2^2) / n^2\)
= \((σ1^2 + σ2^2) / n\)
As n approaches infinity, Var(X¯ − Y¯) approaches 0, indicating that the estimator X¯ − Y¯ is consistent.
Therefore, we have shown that X¯ − Y¯ is a consistent estimator of µ1 − µ2.
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Suppose that X1, X2, . . . , Xn and Y1, Y2, . . . , Yn are independent random sample from populations with mean µ1 and µ2 and variances σ(1)^2 1 and σ (2)^ 2 , respectively. Show that X¯ − Y¯ is a consistent estimator of µ1 − µ2.
The Central Limit Theorem is important in Statistics because it allows us to use the normal distribution to make inferences concerning the population mean: O provided that the population from which the sample was drawn is normal and the sample size is reasonably large. O provided that the population size is reasonably large (whether the population distribution is known or not). O provided that the sample size is reasonably large (for any population). o provided that the population from which the sample was drawn is normal.
The correct statement is: provided that the sample size is reasonably large (for any population).
Why the statement provided that the sample size is reasonably large is correct?The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).
Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.
This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters
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The picturegram shows information about CDs sold in a shop.
1 . How manny CDs were sold on Wednesday | Key = 3 |
2. How manny more CDs were sold on Thursday than Wednesday?
**If you know the answer let me know!**
Answer:
i believe number 1 is 18 and number 2 is 9.
Step-by-step explanation:
if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.
Which of the following number lines shows the solution to the compound inequality given below?
-2<3r+4<13
Answer:
We get -2 < r < 3
Corresponding to the fourth choice
The fourth number line is the correct option
Step-by-step explanation:
-2 < 3r+4 < 13
We have to isolate r,
subtracting 4 from each term,
-2-4< 3r + 4 - 4 < 13 - 4
-6 < 3r < 9
divding each term by 3,
-6/3 < r < 9/3
-2 < r < 3
so, the interval is (-2,3)
or, -2 < r < 3
this corresponds to
The fourth choice (since there is no equality sign)
how to work out 109 divided by 200?
Answer:
0.545 your welcome :D
Step-by-step explanation:
109÷200
Answer: 0.545
I just searched it up...... ya welcome homie
Step-by-step explanation:
search it "109 divided by 200" you'll get ur answer
Help me please I don’t know what to do
Answer:
179.3 square units
Step-by-step explanation:
We have to find the area of the rectangle and area of semicircle using the formula and then add the areas.
Area of rectangle:
length = 14 units
width = 10 units
\(\sf \boxed{\text{\bf Area of rectangle = length * width}}\)
= 14 * 10
= 140 square units
Area of semicircle:
diameter of semicircle = width of the rectangle
d = 10 units
r = d ÷ 2
= 10 ÷ 2
= 5 units
\(\boxed{\text{\bf Area of semicircle = $\dfrac{1}{2}\pi r^2$}}\)
\(\sf = \dfrac{1}{2}*3.14*5*5\\\\ = 39.26\\\\ = 39.3 \ square \ units\)
Area of the figure = area of rectangle + area of semicircle
= 140 + 39.3
= 179.3 square units
If A and B are sets, show that a ∩ b = a if and only if a ⊆ b.
The statement "a ∩ b = a if and only if a ⊆ b" means that the intersection of sets A and B is equal to set A only if set A is a subset of set B. We can prove this statement using the following steps:
Assume that a ∩ b = a. This means that every element in set A is also in the intersection of sets A and B.Since every element in set A is in the intersection of sets A and B, it follows that every element in set A is also in set B. Therefore, a ⊆ b.Now, assume that a ⊆ b. This means that every element in set A is also in set B.Since every element in set A is in set B, it follows that the intersection of sets A and B contains all of the elements in set A. Therefore, a ∩ b = a.From steps 1-4, we can conclude that a ∩ b = a if and only if a ⊆ b.In conclusion, the statement "a ∩ b = a if and only if a ⊆ b" is true because the intersection of sets A and B is equal to set A only if set A is a subset of set B. This can be proven using the steps outlined above.
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Brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the average? 6 1 3 4 4 4 6 5 5 3 6 4 4 5 2 3 5 4 4 2 a. 14 b. 7 c. 5 d. 4
The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.
What is average?The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.
\(\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}\)
In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.
The average of the 20 times dice rolls,
\(\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}\)
\(\rm Average = \dfrac{80}{20} = 4\)
Thus, the average of the 20 rolls of the dice is 4.
Now, the number of times the result of the dice roll is above 4(x>4) is 7.
Hence, the number of times Brandon rolls above the average is 7.
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What is the slope of the line through (-1,8) and (3,-4)?
Answer:
slope = -3
Step-by-step explanation:
See the pinned image.
Answer:
\(\displaystyle m=-3\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (-1, 8)
Point (3, -4)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: \(\displaystyle m=\frac{-4-8}{3+1}\)[Slope] Subtract/Add: \(\displaystyle m=\frac{-12}{4}\)[Slope] Divide: \(\displaystyle m=-3\)BRAINLIEST. PLEASE ANSWER
Answer:
a). Distance round one loop = 141.37 meters
b). Distance covered = 3534.29 meters
Step-by-step explanation:
Diameter of the given track = 45 meters
a). Distance round one loop of the track = circumference of the circle
Circumference of a circle = π × (Diameter)
= π × (45)
= 141.37 meters
b). Distance covered by going around the track 25 times = 25 × distance in one loop of the track
= 25 × 141.37
= 3534.29 meters
below the paraboloid z = 18 − 2x2 − 2y2 and above the xy-plane
Answer:
y
2
=−
2
z
+7
Steps for Solving Linear Equation
z=18−2×2−2y2
Multiply 2 and 2 to get 4.
z=18−4−2y
2
Subtract 4 from 18 to get 14.
z=14−2y
2
Swap sides so that all variable terms are on the left hand side.
14−2y
2
=z
Subtract 14 from both sides.
−2y
2
=z−14
Divide both sides by −2.
−2
−2y
2
=
−2
z−14
Dividing by −2 undoes the multiplication by −2.
y
2
=
−2
z−14
Divide z−14 by −2.
y
2
=−
2
z
+7
Step-by-step explanation:
the given equation defines a paraboloid that lies below the plane z=0. Specifically, it is situated above the xy-plane, which means that the z-values of all points on the surface are greater than or equal to zero.
we can break down the equation z=18-2x^2-2y^2. This equation represents a paraboloid with its vertex at (0,0,18) and axis of symmetry along the z-axis. The first term 18 is the z-coordinate of the vertex and the last two terms -2x^2 and -2y^2 determine the shape of the paraboloid.
Since the coefficient of x^2 and y^2 terms are negative, the paraboloid is downward facing and opens along the negative z-axis. Therefore, all points on the paraboloid have z-values less than 18. Additionally, since the paraboloid is situated above the xy-plane, its z-values are greater than or equal to zero.
the paraboloid defined by the equation z=18-2x^2-2y^2 is situated below the plane z=0 and above the xy-plane. Its vertex is at (0,0,18) and it opens along the negative z-axis.
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For this question, consider that the letter "A" denotes the last 4 digits of your student number. That is, for example, if your student number is: 12345678, then A = 5678. Assume that the factors affecting the aggregate expenditures of the sample economy, which are desired consumption (C), taxes (T), government spending (G), investment (I) and net exports (NX) are given as follows: Cd= A + 0.6 YD, T= 100+ 0.2Y, G = 400, Id = 300+ 0.05 Y, NX4 = 200 – 0.1Y. (a) According to the above information, explain in your own words how the tax collection changes as income in the economy changes? (b) Write the expression for YD (disposable income). (c) Find the equation of the aggregate expenditure line. Draw it on a graph and show where the equilibrium income should be on the same graph. (d) State the equilibrium condition. Calculate the equilibrium real GDP level.
The correct answer is $56,000.the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables
What is the demand for chairs and tables each day?To determine the total profit for Pinewood Furniture Company, we need to calculate the profit generated from producing 200 chairs and 400 tables.
Each chair generates a profit of $80, and if 200 chairs are produced, the total profit from chairs would be:
200 chairs * $80/profit per chair = $16,000.
Similarly, each table generates a profit of $100, and if 400 tables are produced, the total profit from tables would be:
400 tables * $100/profit per table = $40,000.
Therefore, the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables, would be:
$16,000 (profit from chairs) + $40,000 (profit from tables) = $56,000.
Hence, the correct answer is $56,000.
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please explain so I can understand
Answer:
well im pretty sure its ( 1,1,3)
Step-by-step explanation:
21-1-2
In a sequence of numbers, the first term is x and each term thereafter is twice the previous term. the fifth term is 160. what is the value of x ?
The value of x in sequence of number is 10.
Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.
What is geometric series?
Geometric series is an infinite series of the form:
\(a+ar+a r^{2} +ar^{3} +..........\)
where r is known as common ratio.
Now, first term is x and each term there after is twice the previous term.
So the series will be;
x , 2x , 4x , 8x, ..........
Clearly this series is geometric series with common ratio 2.
And the nth term of geometric series is \(ar^{n-1}\)
⇒ fifth term is 160
\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)
Here, first term is x.
The value of x in sequence of number is 10.
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Fill in the missing number on the table, based on the graph?
Answer:
0.5
Step-by-step explanation:
sana panget kayong lahat
Given the function (Image below) [Algebra ll]
Write 2 decimals that are equivalent to the decimal 9.50?
Please help
Answer: 9.5 and 9.500
Answer:
One would be 9/5 and another could be 1.8
Tekan-Tekan Sdn. Bhd. has order for 200 Model AS-120 calculator for delivery on day 200. The calculator consists of three parts. Components 2 and 3 form subassembly 1 . Sub-assembly 1 and component 4 form the final assembly. Following are the work centers and times of each operation. Table Q3(a) shows routine file of the operation. Assuming: - Only one machine is assigned to each operation - The factory works on 8-hour shift, 5 days a week - All parts move in one lot of 200. (a) Illustrate the backward schedule based on the information given above. (12 marks) (b) Identify when component 3 must be started to meet the delivery date. (2 marks)
Component 3 must be started on day 197 to meet the delivery date of day 200.
To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.
(a) Backward schedule:
Operation | Work Center | Time (hours) | Start Day
--------------------------------------------------------
Final Assembly | Work Center 1 | 1 | 200
Sub-assembly 1 | Work Center 2 | 2 | 199
Component 4 | Work Center 3 | 3 | 197
Component 2 | Work Center 4 | 4 | 196
Component 3 | Work Center 5 | 3 | ????
(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.
From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.
Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.
Hence, component 3 must be started on day 197 to meet the delivery date of day 200.
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Kumi is 16 years old. His father is 44 years old. How many years ago was Kumi's father five times as old as KUMI
Answer:
9
Step-by-step explanation:
4-x = 5(16-x)
44-x = 80-5x
4x = 36
x = 9
Find the measure of x.
40
45°
X
x = [?]
X
Round to the nearest tenth.
Answer:
x ≈ 28.3
Step-by-step explanation:
using the cosine ratio in the right triangle
cos45°= \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )
40 × cos45° = x , then
x ≈ 28.3 ( to the nearest tenth )