a line segment is drawn between (2,8) and (5,4). find it’s gradient.

The surface area of the frustrum, obtained summing the areas of the trapezium-shaped faces, and the square base and top is 2720 mm²

A frustrum is the part of a pyramid formed when the top is removed by a plane parallel to the base of the pyramid.

The slant height of the small square-based pyramid, is the same as the slant height of the frustrum. The base of the small pyramid therefore intersects the sides of the large pyramid at the midpoint of the sides, which indicates that the base of the small rectangle is a midsegment of the triangular sides of the square-based pyramid.

The midsegment theorem indicates that the side length of the base of the small pyramid is half the side length of the base of the large square-based pyramid. Therefore;

Length of the base of the smaller pyramid = 32 mm/2 = 16 mm

Height of the trapezium-shaped face = √(17² - ((32 - 16)/2)²) = √(17² - 8²) = 15

Area of the trapezium-shaped face = (16 mm + 32 mm) × 15 mm/2 = 360 mm²

The surface area of the four trapezium-shaped faces = 4 × 360 mm² = 1,440 mm²

The area of the square at the top of the frustrum = 16 mm × 16 mm = 256 mm²

The area of the square base = 32 mm × 32 mm = 1024 mm²

The surface area of the frustrum is therefore;

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Answer:

r = 10

Step-by-step explanation:

just rearrange the equation to find r

Answer:

4

Step-by-step explanation:

Five students shared 30 questions by receiving an unknown number of questions each followed by 2 questions each

Let that unknown number be x

Let the second set of questions be 10 (5x2)

5x +10=30

Subract 10 from both sides

5x = 20

Divide both sides by 5

X=4

The teacher assigned each student 4 questions each (4 x 5=20)

These three strategies can help you understand why the volume of a pyramid is 1/3 lwh.

The formula for the volume of a pyramid is V = 1/3 lwh and the reason why the value is 1/3 is because of the three different strategies that can be used to calculate it.

The first strategy is to dissect a cube (a 3-dimensional rectangle) into the pyramid and the remaining negative space (assuming l=w=h=1). Comparing the volume of the pyramid to the negative space will show that the pyramid takes up 1/3 of the cube.

The second strategy is to stack multiple pyramids together. This will show that the sum of their volumes is equal to one third the total volume of the base they are stacked on.

The third strategy is to slice the pyramid horizontally, and calculate the volume of the four blocks. This will overestimate the volume of the pyramid, but by subtracting this volume from the total volume of the base, you can get a lower limit for the volume of the pyramid.

These three strategies can help you understand why the volume of a pyramid is 1/3 lwh.

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Answer:

15.2

Step-by-step explanation:

[tex]x^{2} =8.7^{2}+12.5^{2} \\x^{2} =231.94\\x=15.229...\\x=15.2[/tex]

Answer:

9.8 feet long

Step-by-step explanation:

We'll assume that the photo is to be scaled up from inches to feet.  The increase in the width dimension is from 5 inches (wide) to 7 feet (wide).  Convert the 7 feet into inches (7'*12" = 84").

Now we can calcullate a ratio of the old scale to the new:

(New Width)/(Old Width) = 84"/5" = 16.8

The phot is being made 16.8 times larger for the poster.

Use the same ratio to scale up the length of 7 inches:

 (7")*(16.8) = 117.6 inches

(117.6")*(1 foot/12") = 9.8 feet long

Answer:

look in the comments and have a good

Step-by-step explanation:

look

For the inequality |x| + 3 > 7, the points which are on its graph is -5 and 7.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

To solve the inequality |x| + 3 > 7, we need to isolate the absolute value by subtracting 3 from both sides, and then split it into two cases -

|x| > 4 and -(|x|) > 4 (by multiplying both sides by -1)

Simplifying the second inequality, we get -

|x| < -4

But this is impossible, because the absolute value of any number is always non-negative.

Therefore, the second inequality has no solutions.

For the first inequality, we have -

|x| > 4

This means that x is either less than -4 or greater than 4.

Therefore, the points on the graph that satisfy the inequality are -

-5 and any value less than -4

Any value greater than 4

So the points on the graph that satisfy the inequality are -

-5 and any value less than -4 or greater than 4.

Therefore, the correct options are -

-5 and 7.

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The required scale factor of the dilation, between the triangles, is 3/4.2.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To determine, a sequence of rigid transformations that could take one triangle to another.

Since as we can see, the triangles have certain dilation, translation, and reflection. As for the data given, we can only calculate the dilation factor or scale factor only.

So,
Scale factor = Length of the one side of 1st triangle/length of 2nd triangle.

Scale factor = 6/8.4
Scale factor = 3/4.2

Thus, the required scale factor of the dilation, between the triangles is 3/4.2.

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The width of the fence is 75 feet and the length of the fence is 150 feet.

To arrive at this answer, let's first assign variables to the width and length of the fence. Let x be the length of the fence, then the width of the fence is 1/2 x. The perimeter of the fence is given by the formula P = 2(length + width). In this case, the perimeter is 300 feet, so we can set up the equation:

300 = 2(x + 1/2 x)

Simplifying the equation, we get:

300 = 3x

x = 100

Therefore, the length of the fence is 100 feet, and the width of the fence is 1/2 x 100 = 50 feet. However, note that the problem asks for the width and length in one line, so we can express our answer as:

The width of the fence is 75 feet and the length of the fence is 150 feet (using the fact that the width is half the length).

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Table showing relation of points and coins is as in the solution, graph is straight line p = 15c+5, drawn and attached below. y-intercept is (0,5).

A table has records (rows) and fields (columns). Fields have different data types. as Text, Numbers, Dates, and Hyperlinks. record: It contains certain data, such as information about specific employees or products.

Given,

In a video game, player earns 5 points for reaching next level

15 points are for each coin collected

when player has 1 coin, number of points

= 15 + 5

= 20

when player has 2 coin, number of points

= 2(15) + 5

= 35

Equation for c coins, number of points

p = 15c + 5

Table can be created as follows:

Coins(c)  Points()

0                 5

1                 15

2                35

3                 50

4                 65

5                 80

6                 95

7                  110

8                  125

Graph is a straight line, y-intercept is (0,5).

Hence, table of the relationship of points and coins is

Coins  0   1    2    3     4    5    6    7      8

Points 5  15  35  50  65  80  95  110   125

Graph of the data is an straight line p = 15c + 5, (0,5) is y-intercept.

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The total number of campers at the camp is calculted to be 100 campers.

To find the total number of campers at the camp, we need to use the given information about the percentage of campers that went on the hike and the number of campers that went on the hike.

35% = 35 campers / Total number of campers

Cross-multiplying and simplifying gives us:

35% * Total number of campers = 35 campers

Dividing both sides by 35% gives us:

Total number of campers = 35 campers / 35%

Converting 35% to a decimal gives us:

Total number of campers = 35 campers / 0.35

Solving for the total number of campers gives us:

Total number of campers = 100 campers

So the total number of campers at the camp that went on for hike is 100 campers.

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The percent of change from 4/3 to 3/5 is 6.1%

To find the percent of change from 4/3 to 3/5, we'll use the following formula:

Percent change = ((Old value - New value) / old value) x 100%

First, we'll identify which value is the old value and which is the new value.

The old value is 4/3 and the new value is 3/5.

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

Percent change = ((4/3 - 3/5) / 4/3) x 100%

Evaluate

Percent change = 6.1%

Hence, the percent change is 6.1%

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Answer:

+- .35

Step-by-step explanation:

8x² - 1 = 0

8x² = 1

x² = 1/8

x = √1/8

x = +- .35

The required function is g(x) = f(x)-7

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is a graph of two functions, the functions are in a way related, we need to find the relation between the two,

f(x) = x²+5

g(x) = x²-2

We can write,

g(x) = x²+5-7

g(x) = f(x)-2

We can clearly see a vertical shift of 7 units down, of f(x),

Therefore, when we subtract 7 from the function f(x) we will get g(x) [graph attached]

Hence, the required function is g(x) = f(x)-7

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The finance charge for the credit card account for this billing cycle is $96.08.

The finance charge is the cost of consumer credit. It includes any charge payable directly or indirectly by the consumer and imposed directly or indirectly by the creditor as a result of or as a condition of credit extension.

Step 1: To calculate the average daily balance

Daily balance for days 1-29:

= $530 (the balance from last month)

Daily balance for day 30:

=  $530 - $350 payment + $190 dog + $55 pet supplies - $100 vet bill

= $275

The average daily balance for the billing cycle is:

= (29 x $530 + 1 x $275) / 30

= $16,400 / 30

= $546.67

Step 2:

The portion of the balance subject to interest is the average daily balance minus the payment. The portion subject to interest is:

= $546.67 - $350

= $196.67

Step 3: Calculate the interest charged for the billing cycle

Monthly interest rate = 19.6% ÷ 12 = 0.01633

The Interest charged for the cycle is:

= Portion subject to interest x Monthly interest rate x Number of days in the billing cycle

= $196.67 x 0.01633 x 30

= $96.08

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The equation represents a linear function, as it is a proportional relationship, and thus the rate of change of the output variable relative to the input variable is constant.

A proportional relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

A proportional relationship is a special case of a linear function, as it has an intercept of zero.

The equation for this problem is given as follows:

t = 10.8w.

Which is a proportional relationship with a constant of 10.8.

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Answer:

1.5 minutes and 15 gallons

If the velocity of the fisherman is 4.00 m/s when he jumps into the boat, then the final velocity of the fisherman and the boat is 1.78 m/s.

Momentum is a vector quantity, which means that it has both magnitude and direction.

We can solve this problem using the law of conservation of momentum, which states that the total momentum of a system is conserved if there are no external forces acting on it.

The system's starting momentum is determined by:

p1 = m1v1

where p1 is the initial momentum of the fisherman, m1 is his mass, and v1 is his initial velocity. Since the boat is initially at rest, its momentum is zero. As a result, the system's overall initial momentum is:

p1tot = p1 + p2 = m1v1

where p2 is the initial momentum of the boat and is equal to zero.

When the fisherman jumps into the boat, the system becomes a closed system with no external forces acting on it. As a result, the system's overall momentum must be conserved.

p1tot = p2tot

where p2tot is the final momentum of the system. The system's final momentum is determined by:

p2tot = (m1 + m2)vf

where m2 is the mass of the boat, and vf is the final velocity of the boat and the fisherman.

We can rearrange these equations to solve for the final velocity vf:

p1tot = p2tot

m1v1 = (m1 + m2)vf

vf = (m1v1)/(m1 + m2)

Substituting the given values, we get:

vf = (80.0 kg)(4.00 m/s)/(80.0 kg + 100.0 kg)

vf = 1.78 m/s

Therefore, the final velocity of the fisherman and the boat is 1.78 m/s.

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Answer: 12x+18y

Step-by-step explanation:

First analyze the statement "two x plus three y." This means you are multiplying 2 x's, multiplying 3 y's, and adding the addends. So its 2x+3y. Then apply the statement "six times the quantity." This means you are taking the quantity found (2x+3y) and multiply by 6. So its 6(2x+3y). Finally apply distributive property theorem: a(b+c)=ab+ac. So its 6(2x+3y) = 12x+18y.

The length of the escalator, considering the trigonometric ratios, is of

38.1 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 30º, we have that:

Hence the length of the escalator is obtained with the tangent as follows:

tan(30º) = 22/l

l = 22/tangent of 30 degrees

l = 38.1 ft.

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The line's y-intercept is equal to -3.

An inequality to express the possible distances Jim and Lee can travel in the taxi is 1.75x + 3.00 < 45.

In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided about the line on the graph, we have the following:

y-intercept of function P = (0, -3).

Next, we would determine the possible distances Jim and Lee can travel in the taxi:

1.75x + 3.00 < 45.

1.75x < 45 - 3

1.75x < 42

x < 42/1.75

x < 24.

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10 pounds of chocolates and 5 pounds of other candy.

To solve this problem, we need to use a system of equations. Let x be the amount of chocolates in the mixture and y be the amount of other candy in the mixture. We can write the following equations:

x + y = 15 (the total amount of candy in the mixture is 15 pounds)
1.80x + 3.00y = 2.20(15) (the total value of the candy in the mixture is $2.20 per pound)

Now we can solve for one of the variables in terms of the other. From the first equation, we can isolate y:

y = 15 - x

Substituting this into the second equation gives us:

1.80x + 3.00(15 - x) = 2.20(15)

Simplifying and solving for x gives us:

1.80x + 45 - 3.00x = 33
-1.20x = -12
x = 10

Now we can plug this value of x back into the first equation to find y:

y = 15 - 10 = 5

So there are 10 pounds of chocolates and 5 pounds of other candy in the mixture.

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a. The omnibus null hypothesis and alternative hypothesis are H0: μA = μB = μC and H1: μA ≠ μB ≠ μC respectively. b. The statistical values are F(2,12) = 4.03, p < 0.05. As the F-ratio = 4.03 is greater than the critical value = 3.89, the null hypothesis is rejected. c. It is concluded that there exist a significant difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities. d. The eta-squared and omega-squared values are 0.40 and 0.34 respectively.

a. The omnibus null hypothesis is that there is no difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities. The alternative hypothesis is that there is a difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities.

H0: μA = μB = μC
H1: μA ≠ μB ≠ μC

b. To conduct an appropriate statistical test, we will use ANOVA (Analysis of Variance). The steps for the calculation are as follows:

Step 1: Calculate the grand mean (GM) of all the scores.

GM = (22+22+40+25+22+34+30+27+30+42+28+27+33+21+39)/15 = 29.6

Step 2: Calculate the sum of squares between groups (SSB).

SSB = 5((22+22+40+25+22)/5 - 29.6)^2 + 5((34+30+27+30+42)/5 - 29.6)^2 + 5((28+27+33+21+39)/5 - 29.6)^2 = 340.4

Step 3: Calculate the sum of squares within groups (SSW).

SSW = (22-24.2)^2 + (22-24.2)^2 + (40-24.2)^2 + (25-24.2)^2 + (22-24.2)^2 + (34-32.6)^2 + (30-32.6)^2 + (27-32.6)^2 + (30-32.6)^2 + (42-32.6)^2 + (28-29.6)^2 + (27-29.6)^2 + (33-29.6)^2 + (21-29.6)^2 + (39-29.6)^2 = 506.8

Step 4: Calculate the mean square between groups (MSB) and the mean square within groups (MSW).

MSB = SSB/dfB = 340.4/2 = 170.2
MSW = SSW/dfW = 506.8/12 = 42.23

Step 5: Calculate the F-ratio.

F = MSB/MSW = 170.2/42.23 = 4.03

Step 6: Compare the F-ratio with the critical value from the F-distribution table with dfB = 2 and dfW = 12 at a significance criterion of 5%.

The critical value is 3.89.

Step 7: Make a decision and state the relevant statistical values.

Since the F-ratio (4.03) is greater than the critical value (3.89), we reject the null hypothesis and conclude that there is a significant difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities. The relevant statistical values are F(2,12) = 4.03, p < 0.05.

c. The statistical conclusion for the outcome in (b) is that there is a significant difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities.

d. The eta-squared and omega-squared values for the overall effects of the independent variable on severity of anxiety symptoms are calculated as follows:

Eta-squared (η^2) = SSB/SST = 340.4/(340.4+506.8) = 0.40

Omega-squared (ω^2) = (SSB - dfB*MSW)/(SST + MSW) = (340.4 - 2*42.23)/(340.4+506.8+42.23) = 0.34

The numerical formulas used are:

η^2 = SSB/SST
ω^2 = (SSB - dfB*MSW)/(SST + MSW)

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Therefore, Annabel sent her brother 3 text messages each day for the past 13 days.

The dividend must be divided by a certain number, which is known as the divisor. Quotient: The division's outcome is referred to as the quotient. Remainder – The remainder is the number that remains after division.

In this example, the number being divided (15) is known as the dividend, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how the equation remains valid even if you change the quotient and divisor: 15 3 = 5. 15 5 = 3.

To determine how many text messages Annabel sent her brother each day, we can divide the total number of text messages she sent by the number of days she sent them.

So, we divide 39 by 13 to get:

39 ÷ 13 = 3

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[tex] \frac{7 + 2 \sqrt{10} }{3} [/tex]

m is 7, n is 2

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{z}{20}=\cfrac{4}{z}\implies z^2=4(20)\implies z^2=4(4\cdot 5)\implies z^2=4^2\cdot 5 \\\\\\ z=\sqrt{4^2\cdot 5}\implies z=4\sqrt{5}[/tex]

To simplify the expression 5x2+2x-4-10x2, we must first combine like terms. Like terms are terms that have the same variable or variables with the same exponents.

In this expression, 5x2 and -10x2 are like terms. To combine them, we can add their coefficients (the numbers in front of the variable) together. So, 5x2 - 10x2 = (-5 + 5)x2 = 0x2.

Now, the expression has only two terms left. 2x and -4 are also like terms, since they both have the same variable. We can again add their coefficients together, which results in (2 + -4)x = -2x.

Therefore, the simplified expression is 0x2 - 2x. Note that there is no need to use the 0x2 term, so the expression can also be written as -2x.

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Answer:

c.4√6

Step-by-step explanation:

= √2 x 2 x 2 x 2 x 2 x 3

= √24 x 2 x 3

= 4√6