In which type of triangle is the orthocenter on the perimeter of the triangle?

a right triangle
an acute triangle
an obtuse triangle
an equilateral triangle

Answer:

The measure of angle GDE is 32 degrees

Step-by-step explanation:

Part 16) we know that

If DG is the angle bisector of angle FDE

then

m∠1=m∠2 (both angles are equal)

substitute the given values

[tex](7x+4)\°=(9x-4)\°[/tex]

solve for x

[tex]9x-7x=4+4[/tex]

[tex]2x=8[/tex]

[tex]x=4[/tex]

Remember that

m∠GDE=m∠1

m∠1=(7x+4)°

substitute the value of x

m∠1=7(4)+4=32°

therefore

The measure of angle GDE is 32 degrees

Answer:

Attached

Step-by-step explanation:

She bikes 761.25 miles in all to and from her job in 29 weeks.

Step-by-step explanation:

Distance from her house = 2.625 miles

As this is the distance of one side, she covers same distance for coming back.

Total distance for one day = 2.625 + 2.625 = 5.25 miles

She goes to work for 5 days per week.

29 weeks = [tex]29*5 = 145\ days[/tex]

Total distance covered in 29 weeks;

Total distance = Distance for one day * Days in 29 weeks

[tex]Total\ distance=5.25*145=761.25\ miles[/tex]

She bikes 761.25 miles in all to and from her job in 29 weeks.

Keywords: multiplication, distance

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Answer:

The pictures Melcher take out the family room were 77 pictures.

Step-by-step explanation:

Given:

Melchers digital camera can hold about 430 pictures, He used 18% of the mirror memory card while taking pictures at family reunion.

Now, to get number of pictures Melcher take out the family room:

Number of pictures Melcher take = 18%  of total number of pictures camera can hold.

                                                             [tex]=\frac{18}{100}\times 430[/tex]

                                                             [tex]=0.18\times 430[/tex]

                                                             [tex]=77.4[/tex]

So, number of pictures Melcher take = 77.4

Now, rounding to the nearest whole number = 77.

Therefore, the pictures Melcher take out the family room were 77 pictures.

Answer:

178 m

Step-by-step explanation:

The area of a square is the square of one of its sides, so the square root of the area is the length of one of its sides.

√31684 = 178

Since you know the area of a square is lengh times width,

you can do…

length x width= 31684

but since you know that length=width

it is just length squared=31684

so,

length= square root of 31684

at the end length of each side of a square are the the same so, if you know one then you know all of the others,

so,

length of each side in this square is=178 meters

The number of adults = 41

The number of children = 97

Step-by-step explanation:

Let x be the number of adults and

y be the number of children

then according to the given conditions

[tex]x+y = 138\ \ \ Eqn\ 1\\11x+4y = 839\ \ \ Eqn\ 2[/tex]

From equation 1:

x = 138-y

Putting in equation 2

[tex]11(138-y)+4y = 839\\1518-11y+4y = 839\\1518 -7y = 839\\-7y = 839-1518\\-7y = -679\\[/tex]

Dividing both sides by -7

[tex]\frac{-7y}{-7} = \frac{-679}{-7}\\y = 97[/tex]

Putting y = 97 in equation 1

[tex]x+ 97 = 138\\x = 138-97\\x = 41[/tex]

Hence,

The number of adults = 41

The number of children = 97

Keywords: Linear equations variables

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Answer:

x = 85

Step-by-step explanation:

There are two triangles. For the purpose of communication, I label them as right triangle and acute triangle.

All triangles' interior angles must add to 180°.

Since we already have two of the three angles in the acute triangle, we can find the third angle, which I label as "y":

180° = 25° + 60° + y

180° = 85° + y

180° - 85° = 85° - 85° + y

y = 95°

Supplementary angles are angles that add to 180°. This is true of any straight lines.

In this question, the angles x and y are supplementary because they make up a straight line.

x + y = 180°

x + 95° = 180°

x = 85°

Without all these steps, we can also figure out that x = 85 by adding 60° and 25° because the sum of a triangles' two interior angles are equivalent to the supplementary of the third angle.

James has 55 dimes in the bag

Step-by-step explanation:

The given is:

We need to find how many dimes James has

Assume that the number of nickels is x and the number of

dimes is y in the bag

∵ There are x nickels in the bag

∵ There are y dimes in the bag

∵ There are 77 coins in the bag

∴ x + y = 77 ⇒ (1)

∵ 1 nickel = 5 cents

∴ The value of nickles in the bag = 5x cents

∵ 1 dime = 10 cents

∴ The value of dimes in the bag = 10y cents

∵ The total value of coins is $6.60

∵ 1 dollar = 100 cents

∴ $6.60 = 6.60 × 100 = 660 cents

∴ 5x + 10y = 660 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -770 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -110

- Divide both sides by -5

∴ x = 22

Substitute the value of x in equation (2) to find y

∵ 22 + y = 77

- Subtract 22 from both sides

∴ y = 55

∴ The number of dimes is 55

James has 55 dimes in the bag

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Answer:

This is correct I did it on schoology

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

The number of kids who brought their lunches is 3/7 of 84.

3/7 of 84 = 3/7 * 84 = 3/7 * 84/1 = (3 * 84)/(7 * 1) = 252/7 = 36

36 kids brought their lunches.

9 of the 36 kids got a slice of pizza.

The fraction is 9/36 = 1/4

Answer: 1/4

Answer:

Find the question in the attachment below.

Number of tickets sold on Saturday [tex]=6986[/tex]

Number of tickets sold over the days [tex]=9640[/tex]

Step-by-step explanation:

a.

Number of tickets sold on Saturday

Twice as many as the number of adult tickets [tex]=2\times 976= 1952[/tex]

Three times as many as the number of children's tickets [tex]3\times 1678=5034[/tex]

Total number of tickets sold on Saturday =[tex](1952+5034)=6986[/tex]

b.

Total number of tickets sold on Friday and Saturday

Summation of adult and children's ticket on both the days.

[tex]=(6986+976+1678)=9640[/tex]

So total tickets sold on Saturday is [tex]6986[/tex] and tickets sold on both days [tex]=9640[/tex]

Answer:

[tex]\displaystyle y = \frac{4}{5}x[/tex]

B. x 1 3 4 5

y 50 150 200 250

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{0 + 24}{0 + 30} = \frac{24}{30} = \frac{4}{5} \\ \\ y = \frac{4}{5}x[/tex]

We can write the equation from here, since both the x-intercept and y-intercept are at the origin.

_______________________________________________

Now, all you have to do is input each value into the function to confirm their authenticities. Once you do this, you WILL arrive at answer choice B).

I am joyous to assist you anytime.

Answer:

9x^4 - 22 is the answer . hope this helps!

Answer:

The correct answer is B. Exponential form.

Step-by-step explanation:

The exponential form was developed to express repeated multiplications and to make it easier to write long numbers. The exponential notation has two parts. The base, as the name says, is the number below. The other part of the notation is a small number written on the superscript to the right of the base, called an exponent. We will use an example to learn about the exponential form or notation.

2³

In this example the base is 2. This means that 2 is a factor, and that it will be multiplied by itself a certain number of times. The precise number of times is given by the exponent, the number in the superscript. In this case, the exponent is 3, which means that base 2 will be used as a factor 3 times. So  2³ means 2 • 2 • 2 and the result is 8.

Answer:D

Step-by-step explanation:

factorise 2x²-16x+32

x²-8x+16

(x-4)²

factorise 4x²-2x-20

2x²-x-10

2x²+4x-5x-10

2x(x+2)-5(x+2)

(2x-5)(x+2)

solving for (f/g)(x)

(x-4)²/(x+2)÷(2x-5)(x+2)/(x-4)²

(x-4)²/(x+2)*(x-4)²/(2x-5)(x+2)

(x-4)⁴/(2x-5)(x+2)²

Step-by-step explanation:

What's the question here, ik how to do this pretty well

Answer:

26

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

Answer:

27 miles.

Step-by-step explanation:

The distance between two points ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) on the coordinate plane are given by the formula

[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}  }[/tex]

Therefore, the distance between points (12,6) and (12,15) is [tex]\sqrt{(12 - 12)^{2} + (15 - 6)^{2}} = 9[/tex] units

Again, the distance between the points (12,15) and (4,0) is [tex]\sqrt{(4 - 12)^{2} + (0 - 15)^{2}} = 17[/tex] units

And the dictance between the points (4,0) and (12,6) is [tex]\sqrt{(12 - 4)^{2} + (6 - 0)^{2}} = 10[/tex] units

Therefore, the total distance is (9 + 17 + 10) = 36 units.

If each unit on the coordinate plane represents 0.75 miles, then Tony rides on the city bus by (36 × 0.75) =27 miles. (Answer)

The ordered pair for Y is (-4,-2)

Step-by-step explanation:

Given

X(-2,3)

Z(-6,-7)

As Y is the mid-point of XZ, it will divide Xz in two equal segments. Y is the mid-point of the segment.

Let (x_Y, y_Y) be the coordinates of the mid-point

Then

[tex](x_Y, y_Y) = (\frac{x_1+_2}{2} , \frac{y_1+y_2}{2})[/tex]

Putting the values

[tex]=(frac{-2-6}{2} , \frac{3-7}{2})\\=(\frac{-8}{2} , \frac{-4}{2})\\=(-4, -2)[/tex]

Hence,

The ordered pair for Y is (-4,-2)

Keywords: Coordinate geometry, Mid-point

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The store charges $8 for one red dot CD and $10 for one green dot CD.

Step-by-step explanation:

Given,

Red dot CDs = r

Green dot CDs = g

According to given statement;

4r+2g=52   Eqn 1

3r+g=34    Eqn 2

Multiplying Eqn 2 by 2;

[tex]2(3r+g=34)\\6r+2g=68\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 1 from Eqn 3

[tex](6r+2g)-(4r+2g)=68-52\\6r+2g-4r-2g=16\\2r=16[/tex]

Dividing both sides by 2;

[tex]\frac{2r}{2}=\frac{16}{2}\\r=8[/tex]

Putting r=8 in Eqn 2

[tex]3(8)+g=34\\24+g=34\\g=34-24\\g=10[/tex]

The store charges $8 for one red dot CD and $10 for one green dot CD.

Keywords: linear equation, subtraction

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By setting up and solving a system of linear equations based on the information that Collette bought 2 green-dot and 4 red-dot CDs for $52, and Jakara bought 3 red-dot CDs and 1 green-dot CD for $34, we determined that the price of each green-dot CD is $10 and each red-dot CD is $8.

Collette and Jakara went shopping at a local music store which had CDs marked with a red dot, r, at one price and CDs marked with a green dot, g, at another price. Collette bought 2 green-dot CDs and 4 red-dot CDs for $52, and Jakara bought 3 red-dot CDs and 1 green-dot CD for $34. To determine the prices for each type of CD, we set up a system of equations based on the information provided:

2g + 4r = 52 (Equation 1: Collette's purchase)

1g + 3r = 34 (Equation 2: Jakara's purchase)

We can solve this system of equations using either the substitution or the elimination method. In this answer, we will use the elimination method.

Multiply Equation 2 by 2 to align the coefficients of g: 2g + 6r = 68

Subtract Equation 1 from the new version of Equation 2 to eliminate g: (2g + 6r) - (2g + 4r) = 68 - 52

This simplifies to 2r = 16, so divide by 2 to find r: r = 8

Use the value of r to solve for g in Equation 1: 2g + 4(8) = 52

This simplifies to 2g + 32 = 52, so subtract 32 from each side: 2g = 20

Finally, divide by 2 to find g: g = 10

Therefore, the price of a green-dot CD is $10 and the price of a red-dot CD is $8.

In a kite, generally there is only 1 line of symmetry which runs from the vertex angle where the two sides of unequal length meet to the vertex angle directly opposite. Therefore, in the case of kite ABCD, the correct answer is option A) 1 line of symmetry.

In the field of mathematics, a kite is a quadrilateral shape with two pairs of adjacent sides that are the same length. When thinking about the lines of symmetry, you should keep in mind that symmetry means that one half of the figure is a mirror image of the other half. For a kite, the number of lines of symmetry is generally 1. The line of symmetry in a kite runs from the vertex angle where the two sides of unequal length meet, to the vertex angle directly opposite.

This means, in the case of kite ABCD, there is 1 line of symmetry.

So, the correct option is A) 1 line of symmetry.

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Answer:

Step-by-step explanation:

The area of the large sail is 144 square feet.

To find the area of the large sail, we can use the formula for the area of a triangle which is Area = 1/2 * base * height.

In this case, the base of the sail is 12 feet and the height (or the length of the sail) is 24 feet. Plugging these values into the formula, we get:

Area = 1/2 * 12 feet * 24 feet = 144 square feet

Therefore, the area of the large sail is 144 square feet.

The exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6) is:

y = [tex]e^{(ln(13)x)} - 7[/tex].

To find an exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6), we can use the general form of an exponential function:

[tex]y = A * e^{(kx)} + C[/tex]

where A is the initial value, k is the growth/decay rate, e is the base of the natural logarithm (approximately 2.71828), x is the independent variable, and C is the y-coordinate of the horizontal asymptote.

Step 1: Determine the value of C (the y-coordinate of the horizontal asymptote):

Since the asymptote is y = -7, we set C = -7.

Step 2: Use the given points to find A and k:

For point (0, -6):

-6 = A * e⁰ - 7

-6 + 7 = A

A = 1

For point (1, 6):

6 = 1 * [tex]e^{(k*1)[/tex] - 7

13 = [tex]e^{k[/tex]

Step 3: Solve for k:

Take the natural logarithm of both sides: ln(13) = k

Step 4: Write the exponential function:

The exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6) is:

y = [tex]e^{(ln(13)x)} - 7[/tex].

This function will have a horizontal asymptote at y = -7 and pass through the given points (0, -6) and (1, 6).

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The perimeter of a square with side a = 7.2 cm is 28.8 cm. Yes there exists a direct proportional relationship between Side length and Perimeter of square

Given that side of square "a" = 7.2 cm

We have to find the perimeter of square

The perimeter of square is given as:

Perimeter of square = 4a

Where "a" represents the length of side of square

Substituting the given value a = 7.2 cm in above formula, we get perimeter of square

Perimeter of square = 4(7.2) = 28.8 cm

Are the perimeter of the square and the length of its side directly proportional quantities?

[tex]\begin{array}{l}{\text { perimeter of square }=4 a=4 \times \text { length of side }} \\\\ {\frac{\text { perimeter of square }}{\text { length of side }}=4}\end{array}[/tex]

The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.

Two values are said to be in direct proportion when an increase in one results in an increase in the other.

So when length of sides increases, perimeter also increases

Hence perimeter and length of side of square are directly propotional quantities

Step-by-step explanation:

1.10) y = x + 1, x is some even integer

The domain is even integers.  1 plus an even integer is an odd integer, so the range is odd integers.

1.11) y = |x|

The domain is all real numbers.  Since y is the absolute value of x, the range is non-negative numbers (y ≥ 0).

Answer:

There are 2561 girls in the school.

Step-by-step explanation:

2610-49=2561

There are 1331 girls in the school.

Equation is defined as a relation that equates two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given are 49% of students at a school are boys. There are 2610 students at the school.

Assume that there are [x] girls are there. Then, we can write -

x = 2610 - 49% of 2610

x = 2610 - (49/100) x 2610

x = 2610 - 1279

x = 1331

Therefore, there are 1331 girls in the school.

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Answer:

C

Step-by-step explanation:

Using the distributive property of multiplication, we can say that 4x+4y-10 >= x+6y-4. Since we want to solve for y, we'll remove the x from one side (in this case, the left). Subtracting 4x from both sides, we get that 4y-10 >= -3x+6y-4. Separating the y, we can similarly subtract 6y from both sides to get rid of the y on the right and add 10 to both sides to get rid of the 10 on the left, resulting in -2y >= -3x+6. As we want to separate y, we must multiply our inequality by a negative number (-1/2, to be exact, as 1/(-2) = -1/2). However, when we multiply by a negative number, we must flip the sign. Thus, if we multiply both sides by -1/2, our result is y<= 1.5x+3, or C

Answer:

the correct answer is , 4(20+3)

Step-by-step explanation:

Answer:

The difference in slopes of [tex]f(x)\ and\ g(x)[/tex] is = 3

We can say slope of [tex]f(x)[/tex] is positive  and 3 more than slope of [tex]g(x)[/tex] while slope of [tex]g(x)[/tex]  is negative.

Difference of y-intercepts of [tex]f(x)\ and\ g(x)[/tex] is = -7

We can say the y-intercept of [tex]g(x)[/tex] is positive and 7 units above [tex]f(x)[/tex] while y-intercept of [tex]f(x)[/tex]  is negative.

Step-by-step explanation:

Given equation:

[tex]f(x) =2x - 2[/tex]

[tex]g(x) =5-x[/tex]

We need to find the difference of slopes and y-intercepts of the given equations.

The standard form of a slope intercept equation of line is given by:

[tex]y=mx+b[/tex]

where [tex]m[/tex] represents slope and [tex]b[/tex] represents y-intercept of line.

Writing the given equations in standard form to find slope and y-intercept.

[tex]f(x) =2x +(-2)[/tex]

Slope = 2 and y-intercept =-2

[tex]g(x) =(-1)x+5[/tex]

Slope = -1 and y-intercept =5

The difference in slopes of [tex]f(x)\ and\ g(x)[/tex] is = [tex]2-(-1)=2+1=3[/tex]

We can say slope of [tex]f(x)[/tex] is positive  and 3 more than slope of [tex]g(x)[/tex] while slope of [tex]g(x)[/tex]  is negative.

Difference of y-intercepts of [tex]f(x)\ and\ g(x)[/tex] is = [tex]-2-5=-7[/tex]

We can say the y-intercept of [tex]g(x)[/tex] is positive and 7 units above [tex]f(x)[/tex] while y-intercept of [tex]f(x)[/tex]  is negative.

The formula after making t subject of the formula is:

[tex]t = \frac{2-3q}{q+4}[/tex]

Step-by-step explanation:

Given formula is:

[tex]q = \frac{2-4t}{t+3}[/tex]

To make t the subject of the formula we have to isolate t

So,

Cross-multiplying

[tex]q(t+3) = 2-4t\\qt+3q = 2-4t[/tex]

Adding 4t on both sides

[tex]qt+3q+4t = 2-4t+4t\\qt+3q+4t = 2[/tex]

Subtracting 3q from both sides

[tex]qt+3q+4t-3q = 2-3q\\qt+4t = 2-3q[/tex]

Taking t common on left hand side

[tex]t(q+4)=2-3q[/tex]

Dividing both sides by q+4

[tex]\frac{t(q+4)}{q+4}=\frac{2-3q}{q+4}\\t = \frac{2-3q}{q+4}[/tex]

The formula after making t subject of the formula is:

[tex]t = \frac{2-3q}{q+4}[/tex]