Holly's height decreased by 21 is 62.
Use the variable h to represent Holly's height.

Answer:

1. SAS

2. Not congruent

Step-by-step explanation:

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

The solution is,

1. SAS

2. AAS

3. SAS

4. Not congruent.

Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.

here, we have,

we know that,

To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.

Meaning of congruent:

In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.

Two triangles are congruent:

In the case of triangles two factors should be considered:

1) Lengths of each side are equal.

2) Angles are equal.

This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.

now, we have,

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

Hence, 1. SAS

2. AAS

3. SAS

4. Not congruent.

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Answer:

  (b)  area = 29 units²

Step-by-step explanation:

You want the area of the irregular shape shown in the figure.

The area of a rectangular shape is the product of its length and width:

  A = LW

The given shape can be considered to be a 6 unit square with some pieces removed. The area of the remaining shape is the area of that square less the areas of the removed pieces.

The piece removed from the upper left corner is a 2-unit square. Its area is ...

  A = (2 units)(2 units) = 4 units²

The piece removed from the lower right side is 3 units by 1 unit, so its area is ...

  A = (3 units)(1 units) = 3 units²

The area of the square before those pieces were removed was ...

  A = (6 units)(6 units) = 36 units²

Then the area of the remaining shape after the pieces are removed is ...

  Area = 36 units² -4 units² -3 units² = (36 -7) units² = 29 units²

The area of the figure is 29 units².

__

Additional comment

Quite often, the area of an irregular shape is more easily found by subtracting missing areas than by dividing up the existing shape into pieces whose area formulas you know.

The second attachment shows division of the area into smaller rectangles. Working clockwise from upper left, their areas are 1×2, 3×4, 3×1, 3×4, for a total of 2+12+3+12 = 29 square units.

Answer: C

Step-by-step explanation:

The length of the hypotenuse is 11.31 cm

From the question, we have the following parameters that can be used in our computation:

A right, isosceles triangle has its legs to be 8cm

Represen the length of the hypotenuse of the isosceles right triangle  with x

Using the above definition as a guide, we have the following:

x = Leg√2

substitute the known values in the above equation, so, we have the following representation

x = 8 * √2

This gives

x = 11.31

HEnce, the hypotenuse is 11.31 cm

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Answer:

The common factor of all the terms of the polynomial 16x² - 14x is:

2x

Step-by-step explanation:

We are given a polynomial:

16x²-14x

We have to find the common factor of all terms.

First we factorize each term separately and then see the common factor.

16x²=2×2×2×2×x×x

14x=2×7×x

We observe that the common factor is:

2x

Hence,  the common factor of all the terms of the polynomial 16x² - 14x is:

2x

Answer:

2x

Step-by-step explanation:

16 = 2^4

14 = 2 × 7

Common factor of 16 and 14 is 2.

x² = x × x

x = x

Common factor of x² and x is x

The common factor of the two terms is 2x.

Given parallelogram points are (4,3),(-4 3), and (2, -3).

Let's say A= (4,3) , B=(-4 3) ,C=(2, -3) and D=(x, y)

Parallelogram defined as opposite sides are equal and parallel to each other.

From the properties of parallelogram :

We can say diagonals bisect each other.

From this we can easily find 4th point of parallelogram by using mid point concept.

Mid point formula

 (X,Y)=[tex](\frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})[/tex]

Find mid point between AC line

midpoint (X,Y)= [tex](\frac{4 +2}{2},\frac{3-3}{2})[/tex]

                (X,Y)=[tex](\frac{6}{2},\frac{0}{2})[/tex]

                 (X,Y)=(3,0)

Find mid point between BD Line

Mid point (X,Y)= [tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]

Mid point of AC and BD are equal to each other

(3,0)=[tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]

Equate x-coordinate and y-coordinate.

[tex]3=(\frac{-4 +x}{2})[/tex]        and      [tex]0=(\frac{3+y}{2})[/tex]

6=-4+x             and       0=3+y

x=10                 and        y=-3

Therefore ,the coordinates of the 4th point is D(x, y)=(10,-3)

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The coordinates of the fourth point that would complete the parallelogram are (10, -3).

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

We know A, B, and C, where A = (4, 3), B = (-4, 3), and C = (2, -3).

To determine the fourth point, which represents D.

First, we need to find the vector representing side AB.

Subtracting the coordinates of point B from the coordinates of point A. So:

AB = A - B = (4, 3) - (-4, 3) = (8, 0)

Next, we need to find a point that is on the line that is parallel to AB and passes through point C.

The vector CD (where D is the point) is equal to AB. So:

CD = AB = (8, 0)

We know that C = (2, -3),

We can start by adding CD to C to get D:

D = C + CD = (2, -3) + (8, 0) = (10, -3)

Therefore, the coordinates of the fourth point are (10, -3).

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If a cuboid weighs 100N and has sides 5cm by 10cm, then the area of cuboid is 0.005m².

Weight of the cuboid = 100N

Sides of the cuboid = 5cm by 10cm

A solid structure or a three-dimensional shape in geometry is called a cuboid. It is similar to a cube in that a cuboid can become a cube by changing the angles between faces or the lengths of the edges. A convex polyhedron with the same polyhedral graph as a cube is referred to as a cuboid in mathematics.

Calculating the area of the Cuboid -

= 5cm × 10cm

= 50cm²

Converting -

Area of Cuboid

= 50/10000 m²

= 0.005 m²

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The statement must be true are A, B and D.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We are Given that Triangle DKL is congruent to Triangle PVX

We know that when two triangles are congruent then Acc. to CPCT [ Corresponding Parts of Congruent Triangle]

the corresponding parts are also congruent keeping in mind the vertices and the segments are in same comparison as given in the congruent triangles.

(a) Triangle LKD is congruent to Triangle XVP.

(b) Triangle VPX is congruent to Triangle KDL.

(c) Triangle VPX is not congruent to Triangle DLK as according to CPCT, V vertex is not congruent to D, P vertex is not congruent to L and X vertex is not congruent to K.

(d) Angle D is congruent to angle P.

(e) Thus Segment DL is not congruent to Segment PV ( as according to CPCT, Segment DL is congruent to PX and not PV.)

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The measure of angle D is 90 degrees

The sum of the interior angle of a parallelogram is equivalent to 360 degrees

From the information given, the measure of the angles are;

17x + 5, 13x + 7 + 118 and 80

Equate the angles to the sum of interior angles

17x + 5 + 13x + 7 + 118 + 80 = 360

collect the like terms, we get;

30x = 360 - 210

substract the like terms

30x = 150

Make x the subject

x = 5

Hence, the angle is 90 degrees

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The measure for the angle m∠D of the quadrilateral CDEF is equal to 90°

For any quadrilateral, the sum of its four interior angles is equal to 360°, hence we shall calculate for the angle m∠D by first finding the value of x as follows:

17x + 5 + 13x + 7 + 118° + 80° = 360°

30x + 210° = 360°

30x = 360° - 210° {subtract 210° from both sides}

30x = 150°

x = 150°/30

x = 5

m∠D = 17(5) + 5 = 90°

Therefore, the measure for the angle m∠D of the quadrilateral CDEF is equal to 90°.

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In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

A millimeter, abbreviated mm, is the smallest unit for length in the metric, or Standard International, system of measurement. It is used to measure small lengths and for precise measurements. Millimeters can be converted to either units within the metric system or the customary system of measurement.

Divide 8500 kilometers by which 500 km equals 17.5 millimeters.

Therefore, In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

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The orthocenter of ▲ABC is the point (27/4, 17/4)

What is Orthocenter in coordinate geometry?

Any triangle's three altitudes are contemporaneous line segments (they intersect in a single point), and this point is known as the triangle's orthocenter.

To find the orthocenter of ▲ABC, we need to first find the altitude lines of the triangle, which are the perpendicular lines from each vertex to the opposite side. The point where these three lines intersect is the orthocenter.

The slope of this line is:

BC = (-1 - (-4)) / (-1 - 5)

BC = 3/2

Using point-slope form, the equation of the line BC is:

[tex]y -y_{b} = m_{BC} (x - x_{b} )[/tex]

y - (-4) = (3/2)(x - 5)

y = (3/2)x - 17/2

To find the altitude from vertex A to BC, we need to find the equation of the line passing through A and perpendicular to BC. The slope of this line is the negative reciprocal of the slope of BC:

[tex]m\ altitude_A = -2/3[/tex]

The point-slope form of the equation of the altitude from A is:

[tex]y -y_{A} = m_{BC} (x - x_{A} )[/tex]

y - 5 = (-2/3)(x - 5)

y = (-2/3)x + 25/3

Similarly, we can find the equations of the altitudes from vertices B and C to the opposite sides AC and AB, respectively:

Altitude from B to AC:

[tex]m_{AC} = \frac{(y_{C} -y_{A})}{(x_{C} -x_{A})} \\\\m_{AC} = \frac{-3}{2}[/tex]

AC = 2/3

y - (-4) = (2/3)(x - 5)

y = (2/3)x - 2/3

Altitude from C to AB:

[tex]m_{AB} =\frac{(y_{B}- y_{A})}{(x_{B}- x_{A})} \\[/tex]

= (-4 - 5) / (5 - 5)

= undefined

x = -1

Now, we need to find the point of intersection of these three altitudes, which is the orthocenter. To do this, we can solve the system of equations formed by the three altitude lines:

y = (3/2)x - 17/2

y = (-2/3)x + 25/3

y = (2/3)x - 2/3

Substituting the third equation into the first two equations, we get:

(2/3)x - 2/3 = (-2/3)x + 25/3

(4/3)x = 9

x = 27/4

Substituting x = 27/4 into any of the three equations, we get:

y = (2/3)(27/4) - 2/3 = 17/4

Therefore, the orthocenter of ▲ABC is the point (27/4, 17/4).

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Donald and Reynold work at the same rate, the it also takes 8 hours for Donald to make 4 baked zitis.

We know that Reynold can make 4 baked zitis in 8 hours, then his rate of work is:

R = (4 zitis)/(8 hours) = 0.5 zitis per hour.

Whit Donald's help they can make 4 zitis in 4 hours, if we define D as Donald's rate we can write:

(R + D)*4 hours = 4 zitis.

Replacing R we get:

(0.5 zitis/hour + D)*4 hours = 4 zitis

(0.5 zitis/hour + D) = (4 zitis)/(4 hours)

(0.5 zitis/hour + D) = 1 ziti/hour

D = 1 ziti/hour - 0.5 zitis/hour = 0.5 zitis/hour

So Donald works at the same rate than Reynold, then it will take 8 hours for Donald to make 4 baked zitis.

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Referring to the given kite, the length of the other diagonal. DF, is 21 cm.

A kite is a quadrilateral shape, meaning it has four sides. The two pairs of adjacent sides are of equal length, while the opposite sides are not.

The shape of a kite is typically described as having two pairs of congruent adjacent sides that are connected by two diagonal lines that intersect at a right angle. The diagonal lines of a kite are perpendicular to each other, and the shorter diagonal bisects the longer diagonal.

Let's denote the point of intersection of the two diagonals as O.

Since the two diagonal intersect at a right angle, diagonal DF is perpendicular to diagonal EG.

DG = 13 cm

FG = 20 cm

OG = 1/2 EG = 1/2 x 24 = 12 cm

Using the Pythagorean Theorem:

OD = √(DG² - OG²)

     = √(13² - 12²) = 5 cm

OF = √(FG² - OG²)

     = √(20² - 12²) = 16 cm

DF = OD + OF

     = 5 + 16 = 21 cm

The picture in your question is missing, most likely it was like on the attached picture.

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Answer: c

Step-by-step explanation: I got it right

Answer:

Step-by-step explanation:

Find common denominator.

1/x + x-1/9x = 1  => 9/9x + x-1/9x = 1  (The common denominator is 9x.)

Combine like terms.

9 + x - 1 / 9x = 1  =>  x + 8/ 9x = 1

Cancel out 9x from denominator. What you do to one side, you do to the other.

(9x)(x + 8/9x) = 1(9x)  =>  x + 8 = 9x

Solve for x.

8 = 8x  =>  x = 1  (subtract x from both sides at the beginning and then simplify.)

Answer:

Step-by-step explanation:

Method 1: Counting the number of committees with exactly one engineer:

There are 2 ways to choose the engineer, and 10 ways to choose the remaining 9 computer scientists. Hence, there are 2 * 10 = 20 different committees with exactly one engineer.

Method 2: Using the combinations formula:

There are 12 people in total, and we need to choose 10 of them for the committee. We can use the combinations formula to calculate the number of different ways to choose 10 people from 12: C(12, 10) = (12!) / (10! * (12-10)!) = (12!) / (10! * 2!) = 66.

So, there are 66 different ways to create a committee of 10 people with at least one engineer represented.

Answer: 7 + [tex]\frac{B}{5}[/tex] = 3

Step-by-step explanation:

Its pretty simple, just do as the words say. :) the only issue could be "of a number and 5", so you go in order, letting B be the number, it's B/5

The correct weight of butter is 1/32 pounds. Olivia will use 1/32 pound of butter in each batch of muffins.

Olivia has 1/8 pound of butter that she needs to divide equally among 4 batches of muffins. To find out how much butter is used each batch of muffins, we can divide the total amount of butter by the number of batches. So, the amount of butter in each batch of muffins is: 1/8 ÷ 4 batches = 1/32 pound. So, Olivia will use 1/32 pound of butter in each batch of muffins. A pound (lb) is a unit of weight or mass commonly used in the United States and other countries that follow the customary system of measurement.

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Answer: X=2

Step-by-step explanation:

X times 2

1 x 2 = 2

3 x 2 = 6

6 x 2 =12

9 x 2 = 18

Using the value of principal, annual rate and time, the simple interest is $375

Simple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.

The formula for simple interest is:

I = P * r * t

where:

I is the interest amount

P is the principal amount

r is the interest rate (expressed as a decimal)

t is the time period (in years)

In the given problem, we can calculate the simple interest by substituting the values into the formula

A = P(1 + rt)

A = 250(1 + 0.05(10))

A = 375

The simple interest is $375

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Answer:

Step-by-step explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Tony's points can be described by ...

  p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

  p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

  p = p

  12 +10t = 0 +14t . . . . substitute for p in both cases

  12 = 4t . . . . . . . . . . subtract 10t

  3 = t . . . . . . . . . . divide by 4

  p = 14·3 = 42 . . . . the scores after 3 turns

The statement that is true is:

b.) A high correlation can indicate a relationship but cannot prove causation.

Correlation measures the strength and direction of the relationship between two variables, but it does not necessarily imply causation. A high correlation means that there is a strong linear relationship between the two variables, but it does not indicate whether one variable causes the other. There can be other factors that influence the relationship. Therefore, it is important to use other methods, such as experiments or observational studies, to determine causation. Correlation is useful for identifying associations between variables, but it cannot be used as evidence of a causal relationship.

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There is No relation between the variables ggg and hhh.

To determine if the given table shows a proportional relationship between the variables ggg and hhh, we need to check if the ratio of hhh to ggg is constant for all values of ggg.

Let's calculate the ratios of hhh to ggg for each value of ggg:

For ggg = 333, hhh/ggg = 999/333 = 3.

For ggg = 666, hhh/ggg = 363636/666 = 546.

For ggg = 999, hhh/ggg = 818181/999 = 819.

Since the ratios of hhh to ggg are not constant, the given table does not show a proportional relationship between the variables ggg and hhh.

Therefore, the answer is "No, the table does not show a proportional relationship between the variables ggg and hhh."

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A)  The mean of 2018 scores: μ₂₀₁₈ = 75

 The mean of 2019 scores: μ₂₀₁₉ = 75

 The standard deviation of 2018 scores: s₂₀₁₈ = 2.07

 The standard deviation of 2019 scores: s₂₀₁₉ = 5.26

B) The primary difference is that variation is higher in the 2018 season than the 2019 season.

A)

We know that the mean is nothing but the sum of all scores divided by the number of scores.

Thus the mean for 2018 scores is:

μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8

μ₂₀₁₈ = 75

Similarly the mean for 2019 scores is:

μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8

μ₂₀₁₉ = 75

We know that the formula for the standard deviation is:

[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]

where s sample standard deviation

n the size of the sample

[tex]x_i[/tex] each value from the sample

[tex]\bar{x}[/tex] the sample mean

Using this formula, the standard deviation for 2018 scores is:

s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]

s₂₀₁₈ = 2.07

And the standard deviation for 2019 scores is:

s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]

s₂₀₁₉ = 5.26

B)

We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.

Thus, the variation in scores was higher in 2019.

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Find the complete question below.

Answer:

A.  Correct

B.  Correct

C.  Not correct

D.  Correct

E.  Not correct

Step-by-step explanation:

We are told that Michael's race numbers are:

5.25 miles

45.75 minutes

Divide the miles by the minutes to get mIchael's running rate:

0.114754098 mi/min

This result matches option B. " Michael's average pace was about 0.11 miles per minute."

======

Check all the answer options:

A. Michael's unit rate of minutes per mile was about 8.7.  

  Take 0.11475409 mi/min and invert it to find min/mile:

      1/(0.11475409 mi/min) = 8.71 min/mile

This is a correct statement.

B. Michael's average pace was about 0.11 miles per minute.

From above:  This is a correct statement.

C. Michael's unit rate of minutes per mile was about 6.9.

Take the given numbers:   (45.75 minutes)/(5.25 miles) = 8.71 min/mile

This is not a correct statement.

D. Michael's average speed during the race was about 6.9 miles per hour.  

Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:

  Use the conversion factor (60 min/1 hr)

   (0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr

This is a correct statement.

E.  Michael ran about 8.7 miles in 1 minute.

We know from above that he runs at 6.89 miles per hour.  Running 8.7 miles in 1 minute  would mean he is running at (8.7)*(60) = 413 miles/hour.    

Perhaps he had some good energy bars, but the data do not support this conclusion.

This is not a correct statement.

The graph of the linear inequality  [tex]y\geq -3x+4[/tex] is given below.

What is linear inequality?

The expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. A linear inequality, which is an inequality including at least one linear algebraic expression, is when a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1. There are numerous ways to depict various kinds of linear inequalities.

Given linear inequality is [tex]y\geq -3x+4[/tex] for which y region will be in the positive range.

Hence, the graph of the given linear inequality is given below.

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The statement "interpolation is used to determine values beyond a given set of data points" is true

The given statement is " interpolation is used to determine values beyond a given set of data points"

The interpolation is a method in statistics that used to determine or estimate the unknown values in the given set of values. So it is usually used to estimate the price and the potential yield of security

In the interpolation, we use the values from the given set of the data point and estimate the unknown values or values beyond the given set of data points

Therefore, the given statement is true

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Answer:

the domain is: {−3,0,1,6}

the range is:{2,3,4,−6,4}

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Explanation:

In the relation:

{(−3,2),(0,3),(1,4),(1,−6),(6,4)}:

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is:

{−3,0,1,6}

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is:

{2,3,4,−6,4}

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

The solution is, Option A. Line X

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

We have to identify the line which represents the function f(x) = 3x - 5

The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.

In these lines line x is having y-intercept as -5.

Line x passes through (1, 2) and (0, -5)

So slope of the given line will be = y2 - y1/ x2 - x1

= -5-2/ 0-1

= 3

Therefore, option A : Line X is the answer.

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The solution is, the situation can be modeled as y = 52 - 8x.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.

So, the total area to be painted is (28 + 3 × 8) = 52 square meters.

Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as

y = 52 - 8x ................ (1) (Answer)

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