Given that the measure of ∠x is 90°, and the measure of ∠y is 53°, find the measure of ∠z.

In an isosceles triangle with an angle measuring 80°, the other two angles could be 50° each.

An isosceles triangle has two sides of equal length and two angles of equal measure. Since one angle measures 80°, the other two angles must be equal to each other. To find the measure of these angles, we subtract 80° from 180° (the sum of all angles in a triangle) and divide the result by 2. So, each of the other two angles in the isosceles triangle could be 50°.

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The other angles that could be in the isosceles triangle are:[tex]\[\boxed{50^\circ \text{ and } 20^\circ}\][/tex]

In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are equal. The sum of the angles in any triangle is always [tex]\(180^\circ\).[/tex] Given that one angle measures [tex]\(80^\circ\)[/tex], we need to determine the possible configurations for the remaining angles.

Case 1: 80° is the vertex angle

If the [tex]\(80^\circ\)[/tex] angle is the vertex angle (the angle between the two equal sides), the remaining two angles must be equal. Let x be the measure of each of the remaining angles.

Since the sum of the angles in a triangle is [tex]\(180^\circ\):[/tex]

[tex]\[80^\circ + x + x = 180^\circ\]\[80^\circ + 2x = 180^\circ\][/tex]

[tex]\[2x = 100^\circ\][/tex]

[tex]\[x = 50^\circ\][/tex]

So, the other angles in this case are [tex]\(50^\circ\)[/tex] each.

Case 2: 80° is one of the base angles

If the [tex]\(80^\circ\)[/tex] angle is one of the base angles (the angles opposite the equal sides), there will be two such angles. Let y be the measure of the vertex angle.

Since the sum of the angles in a triangle is [tex]\(180^\circ\):[/tex]

[tex]\[80^\circ + 80^\circ + y = 180^\circ\]\[160^\circ + y = 180^\circ\][/tex]

[tex]\[y = 20^\circ\][/tex]

So, the other angles in this case are [tex]\(80^\circ\) and \(20^\circ\).[/tex]

Possible angles

Given that one angle is [tex]\(80^\circ\),[/tex] the possible configurations for the angles in the isosceles triangle are:

- [tex]\(80^\circ, 50^\circ, 50^\circ\)[/tex]

- [tex]\(80^\circ, 80^\circ, 20^\circ\)[/tex]

So, the other angles that could be in the isosceles triangle are:

[tex]\[\boxed{50^\circ \text{ and } 20^\circ}\][/tex]

These are the angles that apply based on the given conditions.

5,103 rounded to the nearest thousands is 5,000

In order to round a number to the nearest thousand, we must see if the digit in the hundreds position is greater or less than 5.

In this case, 1 is less than 5

If the number is less than five, we round the number down, and in this case, to the nearest thousand.

Therefore, the nearest thousand would be 5000

The perimeter of the rectangular pattern, formed by arranging 16 squares with an area of 16 square units in a 4x4 layout, is 16 units.

To determine the perimeter of a rectangular pattern formed by arranging 16 squares, each with an area of 16 square units, in a 4x4 layout, we can follow these steps.

First, we know the area of each square is 16 square units, which means the side length of each square is the square root of 16, which is 4 units.

Now, when these squares are arranged in a 4x4 pattern, you have 4 squares along the length and 4 squares along the width. The length and width, in terms of these squares, are both 4 squares.

The perimeter of a rectangular shape is calculated using the formula: Perimeter = 2 × (Length + Width).

Plugging in the values:

Perimeter = 2 × (4 + 4) = 2 × 8 = 16 units.

So, the perimeter of the resulting figure is 16 units. This means, when you trace the outline of this 4x4 arrangement of squares, the total distance around the shape is 16 units. Each side contributes 4 units, and there are four sides, giving us a total perimeter of 16 units. This calculation follows the basic principles of perimeter for rectangular shapes and applies them to the given arrangement.

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6y-5x=5                                           x=2y+7

x=2y+7                                              x=2(-10)+7

6y-5(2y+7)=5                                     x= -20+7

6y-10y-35=5                                       x= -13

6y-10y=5+35

-4y=40

y= -40/4

y=-10

Final answer:

To solve the given system using substitution, express x from the second equation and substitute into the first, then solve for y. After finding y, substitute it back into the second equation to find x, resulting in x = -13 and y = -10.

Explanation:

Solving Linear Equations Using Substitution Method

To solve the system of linear equations 6y - 5x = 5 and x = 2y + 7 using the substitution method, we first take the second equation, which gives us an expression for x, and substitute it into the first equation.

Step 1: Write the second equation x = 2y + 7.

Step 2: Substitute x in the first equation: 6y - 5(2y + 7) = 5.

Step 3: Expand and simplify: 6y - 10y - 35 = 5 ⇒ -4y = 40 ⇒ y = -10.

Step 4: Now that we have y, we substitute it back into the second equation to find x: x = 2(-10) + 7 ⇒ x = -20 + 7 ⇒ x = -13.

Therefore, the solution to the system of equations is x = -13 and y = -10.

Answer:

Tracie’s bus travels towards her home at an average speed of 1/2 mile per minute.

Step-by-step explanation:

The labels on the graph tell us that the independent variable, x, represents time in minutes, and the dependent variable, y, represents distance from home in miles.

Looking at the graph, we can see that the number of miles from home decreases by 1 for every two minutes.  Since the distance is decreasing, this means that the bus is getting closer to home.  Since it decreases by 1 mile every 2 minutes, this means that the speed is 1/2 mile per minute.

The answer is : A, Tracie's bus travels towards her home at an average speed of 1/2 mile per minute.

f is increasing over the interval 0 < x < 2.

f(2) = 3.

f is decreasing over the interval 2 < x < 5.

In Mathematics and Geometry, a function f(x) is considered as an even function if the following condition holds for all x-values (both positive x-values and negative x-values) in the domain of function f(x):

f(x) = f(-x)  ⇒ symmetrical with y-axis.

This ultimately implies that, a function that is symmetric with respect to the y-axis is an even function.

In this context, we can logically deduce the opposite of this graph would be defined over the interval x ≥ 0. Therefore, we can reasonably infer and logically deduce the following true statements;

f is increasing over the interval 0 < x < 2.

f(2) = 3.

f is decreasing over the interval 2 < x < 5.

Let’s first know what y=mx+b is.

M= slope

B=y-intercept

Since the problem gives us the slope, we can add it in already, which helps us a lot.

y=4x+b

This problem gives us a coordinate. We can substitute the numbers with the values.

3=4(1)+b

3=4+b

-b=4-3

-b=1

b=-1

Now that we have the y-intercept, we now have the hard parts done and now all we do is put it together.

Answer: y=4x-1

To see if it is correct, we can substitute numbers in (like the coordinate) to see if it was right.

3=4-1

3=3

There is your answer!

The first step is to figure out what angle DEB is equal to. Check out the attached image. I've marked this as angle y and it is shown in purple.

Note how the purple angle y and the orange 160 degree angle form a straight angle (180 degrees). So the two angles add to 180. Let's solve for y

(orange angle) + (purple angle) = straight angle

(angle CEB) + (angle DEB) = angle CED

y+160 = 180

y+160-160 = 180-160 ... subtract 160 from both sides

y = 20

----------------------------------

Now we can use this to figure out angle x. The three angles x, 115, and 20, combine to 180 degrees as they all glue together to form a straight angle. Let's solve for x:

x+115+y = 180

x+115+20 = 180 ...replace y with 20

x+135 = 180 ......... combine like terms

x+135-135 = 180-135 ...... subtract 135 from both sides

x = 45

Therefore, the final answer is 45

Answer:

The ordered pair that satisfies the equation is (7, -1)

Step-by-step explanation:

In order to find this, we can solve by subtracting. Start by stacking the two equations on top of one another and subtracting like terms.

3x + 3y = 18

(-) 2x + 3y = 11

--------------------

x = 7

Now that we have the value for x, we can plug in to either equation to find y.

2x + 3y = 11

2(7) + 3y = 11

14 + 3y = 11

3y = -3

y = -1

Final answer:

By applying the method of subtraction to eliminate one variable, we find that the solution to the system of equations 2x + 3y = 11 and 3x + 3y = 18 is x = 7 and y = -3.

Explanation:

Solving a System of Linear Equations

The two linear equations given are:

To find the solution, we can follow a method similar to the one described for solving simultaneous linear equations. We can subtract the first equation from the second to eliminate the variable y:

This gives us x = 7. Now we can substitute x back into either equation to get the value of y:

2(7) + 3y = 11

By solving this, we get y = -3.

The solution to the system of equations is x = 7 and y = -3.

2x + 5 ≤ x - 3

We can treat this like a usual algebraic equation.

Subtract x from both sides.

x + 5 ≤ -3

Subtract 5 from both sides.

x ≤ -8

Thus, x is less than or equal to the quantity -8.

We can test this by plugging in two values into the original inequality: a number greater than -8, and a number less than -8.

2x + 5 ≤ x - 3

We'll use 2 first.

2 * 2 + 5 ≤ 2 - 3

9 ≤ -1 × this is incorrect

Now  we'll use -10

2x + 5 ≤ x - 3

2 * -10 + 5 ≤ -10 - 3

-15 ≤ -13 √ this is correct

Mathematics defines an algebraic equation as a statement in which a relationship between two expressions is established through an equals sign.

For the given question the equation will be:

            [tex]\rm 2x + 5 = x - 3[/tex]

On solving the above equation, x can be defined as -8.

Let the number be x.

According to the question:

Twice of x + 5 =  x - 3

This forms a quadratic equation:

             [tex]\rm 2x + 5 = x - 3[/tex]

The equation  [tex]\rm 2x + 5 = x + 3[/tex] can be solved as follows:

          [tex]\begin{aligned} \rm 2x + 5 &= x - 3\\\\ 2x - x &= -3 - 5\\\\x &= -8 \end[/tex]

Therefore the number is -8.

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B. {-2, 2, 3, 4}

usually in a graph like this, the domain (x) is on the left side, and the range (y) is on the right side.

hope this helps! ❤ from peachimin

30 tens = 30 x 10 = 300

300 ones = 300 x 1 = 300

300 is your answer

30 tens = 30 x 10 = 300

3 hundreds = 3 x 100 = 300

3 is your answer

~Rise Above the Ordinary

Answer:

2 3/4 in

Step-by-step explanation:

The sum of the marked distances is equal to the total distances shown:

... (1 5/8) + ? + (1 5/8) = 6

... ? = 6 - (1 5/8 + 1 5/8) . . . . . subtract the constants on the left

... ? = 6 - (2 5/4) . . . . . . . . . . . add the numbers in parentheses

... ? = 6 - 3 1/4 . . . . . . . . . . . . rewrite the number in parentheses (2+5/4 = 2 + 1 1/4)

... ? = (6 -3) -1/4 = 3 -1/4 . . . . . see below

... ? = 2 3/4

_____

Comment on subtacting mixed numbers

Some folks find it convenient to subtract by adding. To find the difference between 3 1/4 and 6, they would start by adding 3/4 to make 4, then add 2 to make 6. Then they see the difference is 3/4 + 2 = 2 3/4.

Here, I chose to subtract 3 1/4 by subtracting 3, then subtracting 1/4. After subtracting 3 from 6, I get 3, from which I now need to subtract 1/4. It should be clear that taking 1/4 away from 3 will leave 2 3/4. (One of the units has been converted to 4/4 to make the subtraction of 1/4 possible.)

_____

Comment on doubling a fraction

As part of this problem, we needed to add 1 5/8 to itself. We did that by doubling the integer part, and doubling the fraction. When a fraction has an even denominator, it is easy to double it: replace the denominator with half its value — 2×(5/8) = 5/4, where the denominator 4 is half the denominator 8.

No.

An integer is a whole number.

In the case of .634 (or 0.634), we see that it is not a whole number, as there is a decimal point, and numbers to the right of the decimal points.

hope this helps

No, because .634 is an odd number and odd numbers cannot be integers.

In mathematics, the absolute value of a number represents its distance from zero on the number line. If X is a rational number and Y is the opposite of X, their absolute values are the same because they are the same distance from zero, regardless of direction.

In the realm of mathematics, rational numbers have a property called absolute value. The absolute value of a number is its distance from zero on the number line, regardless of direction. So, if X is a rational number, Y being its opposite means it is the same distance from zero, but in the other direction.

For example, if X = 3 (a rational number), then Y = -3 (the opposite of X). Despite X and Y being opposites, their absolute values are the same: |3| = |-3| = 3, as both are 3 units away from zero.

Hence, no matter what values X and Y may have, if Y is the opposite of X (either positive or negative), their absolute values will always be equal because they are the same distance from zero.

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I'm not quite sure what it's asking for you to do but...

_________

Yes, 15 includes 3 and 5, 5 and 3 multiplied is a way to get 15.

The multiple of 15 is 30, 45 and 60.

Yes, 15 is a multiple of each of its factors.

The factors of 15 include 3, and 5. Which is excluding 1 and itself, 15. So, if you ask if 15 is a multiple of its factors, the answer is yes. If you multiply 3 by 5, you get 15. If you multiply 5 by 3, you get 15.

Therefore, we can conclude that 15 is a multiple of its factors.

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Answer:

Sample Response: You need to show that two sides of one triangle are proportional to two corresponding sides of another triangle, with the included corresponding angles being congruent.

Step-by-step explanation:

Different similarity theorems require different information.

The SAS similarity theorem requires two congruent sides and a congruent angle, between the corresponding sides.

The SAS similarity theorem stands for: Side-Angle-Side

This means that:

Hence, the SAS similarity theorem requires two congruent sides and a congruent angle, between the corresponding sides.

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Answer:

[tex]x \leq 40 / 0.25\\ x \leq 160\\[/tex]

Step-by-step explanation:

If the spending limit is $ 40 and making each beads costs $ 0.25, then the amount of accounts you must do  multiplied by the manufacturing cost should not exceed $ 40.

Then the inequation that this restriction would represent is:

[tex]0.25x\leq 40\\[/tex]

Where x is the number of beads made.

This could also be written more specifically:

[tex]x \leq 40 / 0.25\\ x \leq 160\\[/tex]

Therefore the number of beads must be less than or equal to 160

Answer:

Due to decrease in production of tomatoes price will increase.

Step-by-step explanation:

Whenever a commodity whose demand is there in market produce in limited number, it price increases.

Since demand of the tomatoes will remain as usual but limited number of tomatoes will be there in the market so price of the tomatoes will increase. In this way consumer who can afford the price of tomatoes will purchase it and those consumer who can't afford it will not purchase it.

The answer to your question is...

The length of the bike path is 1 5/12 miles.

To find the length of the bike path, we need to determine the total distance Mrs. Escalante travels. She rode 2/3 of a mile and then discovered she still needed to travel 3/4 of a mile. This means she has already traveled a total of 2/3 + 3/4 = 17/12 miles. Let's convert this to a mixed number: 1 5/12 miles. Therefore, the length of the bike path is 1 5/12 miles.

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Answer:

answer is 0.001254.

Step-by-step explanation:

Given that you invested in 3 stocks of Engineering Aces, Upton Clothiers, and Thompson Musical Instruments.

Also given that each stock value is independent of the other.

Let E be the event changing in value by more than 10% in a given week for Engineering Aces,

U be the event changing in value by more than 10% in a given week for Upton Clothiers, and T be the event changing in value by more than 10% in a given week for Thompson Musical Instruments.

Given that P(E) =  = 19%

P(U) = 11%

P(T) = 6%

probability that all three will change by more than 10% in the same week

= P(EUT)

= P(E) P(U) P(T) since three events are independent.

=0.19(0.11)0.06

= 0.001254

Final answer:

The probability that all three stocks, Engineering Aces, Upton Clothiers, and Thompson Musical Instruments, will change by more than 10% in the same week is calculated by multiplying their individual probabilities together, resulting in a probability of 0.1254%.

Explanation:

The question asks for the probability that all three stocks will change by more than 10% in the same week, given their individual probabilities.

To find this probability, since the changes in stocks are independent of each other, we multiply the probabilities of each event occurring together. The formula for the joint probability of independent events is P(E and U and T) = P(E) × P(U) × P(T).

Using the given probabilities:

We calculate:

P(E and U and T) = 0.19 × 0.11 × 0.06

Which equals:

P(E and U and T) = 0.001254 or 0.1254%

Therefore, the probability that all three stocks will change by more than 10% in the same week is 0.1254%.

your answer would b c or $2600

The expected value for this tournament is given as C. $2600

The cost of hosting = 1000

The amount to be gotten if sunny = 4500

The chance that it would rain = 20 percent

4500 - 1000 = 3500

-1000 * 20%

= -200

3500 * (1-20%) = 2800

2800 - 200

= 2600

Hence the expected value that has been solved for the tournament is $2600

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first simplify the inequalities:

3x+2>2  --> x>0   that corresponds to an open circle at 0 and shading to the right

3x <= 6 --> x<=2  that is a closed circle at 2 and shading to the left

together they have shading between open@0 and closed @2 so the

Answer (D) is correct

Answer:

(4,0)

Step-by-step explanation:

The equation of the line is y = (-1/2)x - 2.  At the x-intercept, y = 0. Setting y = (-1/2)x - 2 to zero, we get (1/2)x = 2, and thus x = 4.  

that is the 2nd one Gomez to  Chang

For this one, it is important to know that when it says "under par" think of that as a negative number.  When doing that, here are the choices:

Jones= +3

Chang: -5

Gomez: -2

Harrison: -4

In golf, the lowest score wins, so put the numbers in numerical order from lowest to highest.  Here the answer:

-5, -4, -2, +3

Now match the scores with the corresponding person:

Chang, Harrison, Gomez, and Jones

So A is your answer.

Hope this helps!

The domain of the function is (0, 7) years.

The function that represents the height of the tree is defined over the period during which the tree's height changes. Given that,

The tree starts growing at 0 years (the time when it is first planted). It grows for 4 years, reaching a height of 6 feet by the end of that period.  After 4 years, the tree stops growing and remains at 6 feet for the remaining 3 years. After 7 years total (4 years of growth + 3 years of constant height), the tree is cut down.

The domain of the function that represents the height of the tree is the time interval from when the tree is planted until it is cut down.