Erica is swimming due north at a rate of 7 feet per second. If the current of the lake is 3 feel per second in the direction of S 75° W. find Erica's resultant speed and direction (as a true bearing).

So, the equation of the given curve is a circle centered at (-13, 13) with a radius of 3. Therefore, the correct option is:

[tex](x + 13) ^ 2 + (y - 13) ^ 2 = 9[/tex].

An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal's sign (=). Equations are used to represent a wide range of mathematical and scientific relationships, such as physical laws, chemical reactions, and statistical models. The expressions on either side of the equals sign can contain variables, constants, and mathematical operations, and solving the equation involves finding the value or values of the variables that make the equation true. Equations can take many forms, including linear equations, quadratic equations, trigonometric equations, and differential equations, among others.

To determine which option is correct, we can try to convert the given equation to the standard form of the equation of a circle, which is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

We can complete the square for the given equation by adding and subtracting appropriate constants:

[tex]x^2 + 26x + y^2 - 26y + 329 = 0[/tex]

[tex](x^2 + 26x + 169) + (y^2 - 26y + 169) = -329 + 2(169)[/tex]

[tex](x + 13)^2 + (y - 13)^2 = 9[/tex]

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Accοrding tο the ratiοs, there are 108 dandeliοns in the garden.

A ratiο is a cοmparisοn οf twο quantities οr values, οften expressed as a fractiοn. Ratiοs can be used tο express the relatiοnship between twο οr mοre quantities.

We can use the ratiο οf dandeliοns tο peοnies tο find the number οf dandeliοns when we knοw the number οf peοnies.

The ratiο οf dandeliοns tο peοnies is 12 tο 5, which means that fοr every 12 dandeliοns, there are 5 peοnies.

We knοw that there are 45 peοnies in the garden, sο we can set up a prοpοrtiοn tο find the number οf dandeliοns:

12/5 = x/45

Tο sοlve fοr x, we can crοss-multiply and simplify:

12*45 = 5x

540 = 5x

x = 108

Therefοre, there are 108 dandeliοns in the garden.

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This means that for x values less than or equal to -2, the function equals -2x - 1. For x values between -2 and 1, the function equals x^2 + 2x - 3. And for x values greater than or equal to 1, the function equals 4.

To express the function graphed on the axes below as a piecewise function, we need to analyze the graph and determine the different intervals where the function behaves differently.

Looking at the graph, we can see that the function is a straight line with a slope of 2 when x is less than or equal to -2. Then, the function changes to a parabola that opens upwards when x is between -2 and 1. Finally, the function becomes a horizontal line when x is greater than 1.

Therefore, the piecewise function that represents this graph is:

f(x) =
-2x - 1,    if x ≤ -2
x^2 + 2x - 3,    if -2 < x < 1
4,    if x ≥ 1

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To find the inverse of the function y = x² + 4x + 4, we first replace y with x and x with y:

x = y² + 4y + 4

Next, we rearrange the equation to isolate y on one side of the equation:

x - 4 = y² + 4y

y² + 4y = x - 4

Now, we complete the square by adding (4/2)² = 4 to both sides of the equation:

y² + 4y + 4 = x

We can rewrite the left side of the equation as (y + 2)²:

(y + 2)² = x

Finally, we take the square root of both sides of the equation and solve for y:

y + 2 = ±√x

y = ±√x - 2

Since the original function is not one-to-one, we need to restrict the domain to obtain the inverse function. Specifically, we restrict the domain of the original function to x ≥ -2, since for values of x less than -2 there are two corresponding y-values. Therefore, the inverse function of y = x² + 4x + 4 for this restricted domain is:

y = ±√x - 2, x ≥ -2

Answer:

Let's call the number of nuts "n", the number of bolts "b", and the number of screws "s".

From the problem, we know:

s = 3n (Since there are 3 times as many screws as nuts)

b = n + 32 (Since there are 32 more bolts than nuts)

n + s + b = 782 (Since the total number of nuts, screws, and bolts is 782)

Now we can use substitution to solve for one of the variables in terms of the others. Let's solve for "n":

n + 3n + (n + 32) = 782

5n + 32 = 782

5n = 750

n = 150

Now we know there are 150 nuts. We can use this information to find the number of bolts:

b = n + 32

b = 150 + 32

b = 182

Finally, we can use the information we have about the screws to find their number:

s = 3n

s = 3(150)

s = 450

Therefore, there are 450 screws in the box.

answer 1646

let nuts be-782

screw=3X nuts

bolts = 32 X nuts

Screw=3x782=1646

hope this helps

Answer:

about 7 days

Step-by-step explanation:

31 · .22

6.82 days

rounded up it would be approximately  7 days

The value of p in the equation shown is 0.3

An equatiοn in writing prοving the similarity οf twο phrases. It is made up οf a series οf characters divided intο left and right sectiοns and cοnnected by an equal sign.

Equatiοns are questiοns, and the search fοr methοdical sοlutiοns tο thοse questiοns has fueled the grοwth οf mathematics. Simple algebraic equatiοns with οnly additiοn οr multiplicatiοn tο differential equatiοns, expοnential equatiοns with expοnential fοrmulas, and integral equatiοns are examples οf variοus types οf equatiοns.

The equation that is in the question is given below

p³ = -0.027

or, p=-∛0.027

or, p = -0.3

Hence the value of the p is 0.3

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Mrs. Simcox can make 4 complete batches of snickerdoodles for her class on Pi day, as she has 9 cups of flour and each batch of cookies requires 2 and 1/4 cups of flour.

Mrs. Simcox needs to make snickerdoodles for her class on Pi day and she knows that each batch of cookies requires 2 and 1/4 cups of flour. Therefore, she needs to calculate how many batches of cookies she can make with the 9 cups of flour that she has.

To do this, she divides the total amount of flour she has (9 cups) by the amount of flour required for each batch (2 and 1/4 cups). To simplify this division, she can convert the mixed number (2 and 1/4) to an improper fraction:

2 and 1/4 = (2 x 4 + 1)/4 = 9/4

Therefore, she can rewrite the division as:

9 cups ÷ 9/4 cups per batch

To divide by a fraction, she can multiply by its reciprocal:

9 cups × 4/9 cups per batch = 4 batches

So, Mrs. Simcox can make 4 complete batches of cookies with the 9 cups of flour she has.

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The value of the expression 9 + (20 x one-fourth) – 6 ÷ 2  is 11.

What is PEMDAS?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.

Using PEMDAS (Order of Operations), we perform the operations in the following order:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Applying this to the given expression:

9 + (20 x one-fourth) – 6 ÷ 2

= 9 + (20 x 0.25) - 3 [simplify division first: 6 ÷ 2 = 3]

= 9 + 5 - 3 [simplify multiplication: 20 x 0.25 = 5]

= 11 [simplify addition and subtraction from left to right]

Therefore, the value of the expression is 11.

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Answer:

8 = 83°

Step-by-step explanation:

4 = 2 (Vertically opp. angles)

2 = 8 (Alternate interior angles)

Therefore 4 = 8

Since 4 = 83°

8 = 83°

Answer:

<8 = 83 degrees

Step-by-step explanation:

<4 and <8  are corresponding angles and corresponding angles are equal if lines are parallel

<4 = 83 so <8 = 83

Answer: 5/13

Step-by-step explanation: i did this IXL and got it right

The components of force F1 are F1x = 0N (along the x-axis) and F1y = -10N (along the y-axis).

To determine the components of the two forces acting upon an object with F1 = 10N at a 270° angle with the positive x-axis,

follow these steps:
Step 1: Convert the angle to a standard position
Since the angle is given in degrees and with respect to the positive x-axis, it is already in the standard position.

Step 2: Find the x and y components of F1
To find the components of F1, we'll use trigonometry.

At 270°, the force is pointing straight down along the negative y-axis.

So, the x-component (F1x) is 0, and the y-component (F1y) is -10N.
F1x = F1 * cos(270°) = 10N * 0 = 0N
F1y = F1 * sin(270°) = 10N * (-1) = -10N.

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The result is negative, meaning there is insufficient material to make the curtains without seams.

Each curtain requires 2 1/5 meters of material, so for 8 curtains, the total amount of material required is:

8 x 2 1/5 = 17 3/5 meters

However, Mason's mother only has 16 1/4 meters of material, so she needs to buy more material. The amount of additional material needed is the difference between what she has and what she needs:

17 3/5 - 16 1/4 = 1 2/5 meters

Therefore, Mason needs to buy 1 2/5 meters of material.

To determine how much material is left over, we need to subtract the total amount of material needed for the curtains from the amount of material Mason's mother has:

16 1/4 - 17 3/5 = -1 3/20

In this case, Mason's mother would need to either buy more material or adjust the dimensions of the curtains to fit the amount of material she has.

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Answer: 39

Step-by-step explanation:

x = (56/100) * y

where x is the amount we're trying to find and y is the total amount.

We're given that 56% of this value is $21.84, so we can substitute these values into the equation:

21.84 = (56/100) * y

To solve for y, we can divide both sides by 56/100:

y = 21.84 / (56/100)

Simplifying this expression, we get:

y = 39

Therefore, the number that represents 56% of this value is $21.84.

79 hours will it take for one person to harvest the entire strawberry patch.

The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.

Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.

The strawberry patch's measurements must first be changed from decameters (dam) to meters.

1 decameter (dam) = 10 meter

Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.

The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.

The strawberry patch's area is therefore:

Area of strawberry patch = length × width = 17 m × 14 m = 238 m²

We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:

[tex]\frac{Area of strawberry patch}{ Area picked per hour }[/tex] = a number of hours needed to harvest the complete patch.

The total harvesting time is [tex]\frac{238 m2 }{3 m2/hour}[/tex] = 79.33 hours nearly equal to 79

Therefore, it would take one person 79 hours to gather the complete strawberry patch.

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Using the hypothesis test, the p-value is greater than the significance level, we fail to reject the null hypothesis. There is not enough evidence to suggest that a headed mannequin is more effective in selling clothing.

To perform a hypothesis test to determine if a headed mannequin is more effective in selling clothing, we can use a two-sample proportion test.

Let p1 be the proportion of women who would purchase the dress when presented on a mannequin with a head, and p2 be the proportion of women who would purchase the dress when presented on a headless mannequin.

The null hypothesis is that there is no difference between the two proportions, i.e. p1 = p2, and the alternative hypothesis is that p1 > p2 since we want to test if the headed mannequin is more effective.

We can use a significance level of 0.05. Using the given data, we calculate the test statistic as:

z = (p1 - p2) / √(p × (1-p) × (1/n1 + 1/n2))

where p = (x1 + x2) / (n1 + n2), x1 = 18, x2 = 12, n1 = 50, and n2 = 45.

The calculated z-value is approximately 1.02.

Using a standard normal distribution table, we find the p-value to be approximately 0.155.

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The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4 is  (8/5, (16 + 8j)/5).

We can use the ratio formula for finding the coordinates of the point that divides the line segment AB in the ratio of 1:4:

Let the coordinates of the point dividing the line segment AB be (x, y). Then:

x = (41 + 14)/5 = 8/5

y = (44 + 42j)/5 = (16 + 8j)/5

Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8/5, (16 + 8j)/5).

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The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36 = 0.028

The likelihood that a specific occurrence will occur.

The proportion of the total number of possible outcomes to the number of outcomes in an exhaustive set of equally probable outcomes that result in a particular event.

Two six-sided dice are rolled there are 36 possibilities for outcomes which means 6 possibilities for the first dice and 6 for the second dice.

Therefore 36 is the total possibility outcome.

Count the number of outcomes for the one dice show 5 and the second dice show 6.

There is only one possibility two show the (5, 6) from the total s3 outcomes.

so the probability of rolling a 5 and a 6 i = 1/36 or about 0.028.

Therefore, the total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36.

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Yes, Briony has enough material. She needs 18m of material, which is less than the 19m she has.

To find length of material, we need to calculate the length of each

curtain piece using the given length of material.

To convert a mixed number to an improper fraction, multiply the

denominator (the bottom number) by the whole number, and add the

numerator (the top number).

Now, to convert 2 1/4m into an improper fraction, we multiply the

denominator (4) by the whole number (2), then add the numerator (1).

This gives us (2 × 4) + 1 = 9.

Hence, 2 1/4m can be written as 9/4m.

Since Briony needs 8 pieces of curtain material 2 1/4m in length, she will need a total of:

8 × 2 1/4m = 8 × 9/4m = 18 1/4m.

Briony requires 18 1/4m of curtain material. Since she has 19 m length of

material, she has enough to create 8 pieces of curtain material of 2 1/4m

in length.

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The x-intercept is (12, 0) and the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.

What are the intercepts?

Intercepts are the points where the graph intersects either the x-axis or the y-axis. The x-intercept is the point where the graph intersects the x-axis, which means the y-coordinate of the point is 0. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of the point is 0. To find the intercepts of a function, you can set one of the variables (x or y) to 0 and solve for the other variable. The resulting point will be the intercept.

To find the x-intercept, we set y to zero and solve for x:

x + 7(0) = 12

x = 12

So the x-intercept is (12, 0).

To find the y-intercept, we set x to zero and solve for y:

0 + 7y = 12

y = 12/7

So the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.

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Answer:

30%

Step-by-step explanation:

(156-120) / 120 × 100％

=36 / 120 × 100％

=30%

The logarithmic function y = log(4x-a) is positive for all values of x which are greater than a/4.

A function of this type is a logarithmic function. which can be interpreted as "y equals the log, base b, of x" or "y equals the log of x, base b."

Finding the domain of x that makes the argument (4x-a) of the logarithm positive will help us identify the values of x for which the logarithm in the equation y = log(4x-a) is positive.

Remember that a positive number's logarithm is positive and a negative number's logarithm is indeterminate. (in the real number system).

We must therefore identify the x values that meet the inequality:

4x - a > 0

4x > a

x >a/4

After finding x, we obtain:

x > a/4

The equation y = log(4x-a) therefore has the following domain of x for which the logarithm is positive:

In other words, for all values of x larger than a/4, the expression y = log(4x-a) is defined and positive.

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3 dm is equal to 300 mm, 5 dm is equal to 500 mm, and 2 dm is equal to 200 mm.

To convert 3 dm to mm, we multiply by 10 to get 30 cm, and then by another 10 to get 300 mm.

To convert 5 dm to mm, we multiply by 10 to get 50 cm, and then by another 10 to get 500 mm.

To convert 2 dm to mm, we multiply by 10 to get 20 cm, and then by another 10 to get 200 mm.

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The expressions that are equivalent to 4√5 is

A) 2√20

C) [tex]3\sqrt5+\sqrt5[/tex]

D) [tex]4\times 5^{1/2}[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is [tex]4\sqrt5[/tex].

Now simplifying the given option expressions then,

A) [tex]2\sqrt{20}[/tex] = [tex]2\sqrt{4\times5}[/tex]

= [tex]2\times2\sqrt{5}[/tex]

= [tex]4\sqrt5[/tex]

B) [tex]6^{1/2}-5^{1/2}[/tex]

[tex]= \sqrt6-\sqrt5[/tex]

C) [tex]3\sqrt5+\sqrt5[/tex]

= [tex]4\sqrt5[/tex]

D) [tex]4\times 5^{1/2}[/tex]

[tex]= 4\sqrt5[/tex]

E) [tex]2\sqrt{10}[/tex]

F) [tex]3\times5^{1/2}[/tex]

[tex]=3\sqrt5[/tex]

Hence  the expressions that are equivalent to 4√5 is

A) 2√20

C) [tex]3\sqrt5+\sqrt5[/tex]

D) [tex]4\times 5^{1/2}[/tex]

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The value of A is 9/10.

What is binomial?

Binοmial refers tο a type οf prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial has οnly twο pοssible οutcοmes (success οr failure) and the prοbability οf success is cοnstant acrοss all trials.

The given expressiοn is the sum οf the first several terms οf a harmοnic series. Tο evaluate it, we can use the fοrmula fοr the sum οf the first n terms οf a harmοnic series:

1 + 1/2 + 1/3 + ... + 1/n = ln(n) + γ,

where ln(n) is the natural lοgarithm οf n and γ is the Euler-Mascherοni cοnstant (apprοximately 0.5772).

Using this fοrmula, we can write the expressiοn as:

A = 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/45

= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/9 - 1/10)

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10

= 1 - 1/10

= 9/10

Therefore, the value of A is 9/10.

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Complete Question:

Find The value of A

A=1\3+1\6+1\10+1\15+...+1\45

The passengers selected for the in-flight survey in this scenario can be best referred to as a stratified random sample.

In stratified random sampling, the population is divided into smaller, non-overlapping groups, called strata, which share similar characteristics. In this case, the strata are the 40 flights selected by Northwest Airlines. From each of these strata, a random sample of passengers is chosen, which in this case, is a group of ten passengers from each flight.

This method ensures that each flight's passengers are represented in the survey, allowing for better generalizability of the results. By selecting passengers randomly within each stratum, the survey helps minimize selection bias and ensures that the sample reflects the diversity of the overall population of passengers. The stratified random sampling approach is especially useful when studying a large and diverse population, as it provides a more accurate representation of the population's characteristics compared to simple random sampling.

In summary, the passengers participating in the in-flight survey are best referred to as a stratified random sample because they are chosen from 40 randomly selected flights, with ten passengers randomly selected within each flight. This sampling approach ensures better representation of the overall population and helps minimize selection bias in the survey results.

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The incidence of skin cancer over the two years in the high exposure group is 24.39%.

To calculate the incidence of skin cancer over the two years in the high exposure group, follow these steps:
1. Determine the number of workers in the high exposure group: 800 workers
2. Subtract the initial skin cancer cases in the high exposure group from the total number of workers in the group to find out the workers without skin cancer:

800 - 185 = 615 workers
3. Calculate the number of new skin cancer cases in the high exposure group by subtracting the new cases in the low-exposure group from the total new cases:

175 - 25 = 150 cases
4. Calculate the incidence rate by dividing the new cases in the high exposure group by the number of workers without skin cancer in the high exposure group:

150 / 615 ≈ 0.2439
5. Multiply the incidence rate by 100 to express it as a percentage:

0.2439 * 100 = 24.39%.

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Answer:

392

Step-by-step explanation:

Volume is the area of the base times the height.

Area of the base:

[tex]\frac{(8x14)}{2}[/tex] = 56

Volume:

area of the base times the height

(56)(7) = 392

Helping in the name of Jesus.

By algebra properties, the values of x for each equation are listed below:

Case A: x = 0

Case B: x = 0

Case C: x = 1.584 or x = 1

Case D: x = 1.262 or x = - 0.631

Case E: x = 0.569

Case F: x = 2 or x = 1.322

In this problem we find six cases of equations containing exponential expressions where the value of x must be found. This can be done by means of algebra properties:

Case A

2²ˣ - 2 ˣ⁺¹ + 1 = 0

(2ˣ)² - 2 · 2ˣ + 1 = 0

u² - 2 · u + 1 = 0

(u - 1)² = 0

u = 1

2ˣ = 1

x · ㏒₂ 2 = ㏒₂ 1

x = ㏒₂ 1

x = 0

Case B

3²ˣ - 3ˣ = 0

(3ˣ)² - 3ˣ = 0

3ˣ · (3ˣ - 1) = 0

3ˣ - 1 = 0

3ˣ = 1

x = 0

Case C

2²ˣ - 5 · 2ˣ + 6 = 0

(2ˣ)² - 5 · 2ˣ + 6 = 0

u² - 5 · u + 6 = 0

(u - 3) · (u - 2) = 0

u = 3 or u = 2

2ˣ = 3 or 2ˣ = 2

x = ㏒₂ 3 or x = 1

x = 1.584 or x = 1

Case D

2 · (3²ˣ) - 9 · 3ˣ + 4 = 0

2 · u² - 9 · u + 4 = 0

2 · [u² - (9 / 2) · u + 2] = 0

2 · (u - 4) · (u - 1 / 2) = 0

u = 4 or u = 1 / 2

3ˣ = 4 or 3ˣ = 1 / 2

x = ㏒₃ 4 or x = ㏒₃ (1 / 2)

x = 1.262 or x = - 0.631

Case E

6 · (5²ˣ) - 11 · 5ˣ - 10 = 0

6 · u² - 11 · u - 10 = 0

6 · [u² - (11 / 6) · u - 5 / 3] = 0

6 · (u - 2.5) · (u + 0.667)

u = 2.5 or u = - 0.667

x = 0.569

Case F

2²ˣ⁺¹ - 13 · 2ˣ + 20 = 0

2 · (2ˣ)² - 13 · 2ˣ + 20 = 0

2 · u² - 13 · u + 20 = 0

2 · [u² - (13 / 2) · u + 10] = 0

2 · (u - 4) · (u - 5 / 2) = 0

u = 4 or u = 5 / 2

2ˣ = 4 or 2ˣ = 5 / 2

x = 2 or x = 1.322

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Answer:

Step-by-step explanation:

You want the value of x and the length of side WA in rhombus WART with sides marked 7x-22 and 3x+10.

The sides of a rhombus are congruent, so ...

  7x -22 = 3x +10

  4x = 32 . . . . . . . . add 22-3x

  x = 8

  3x+10 = 3·8 +10 = 34

The value of x is 8, and side WA is 34 units.