A solid oblique pyramid has a triangular base with a length of 8 inches and a height of 6 inches. The slant height of each triangular face is 10 inches. What is the volume of this pyramid?
a) 160 cubic inches
b) 200 cubic inches
c) 240 cubic inches
d) 280 cubic inches

Answer:

[tex]\frac{2.5}{1}[/tex]

Step-by-step explanation:

To express it as a fraction, divide 250 by 100 first to get 2.5. Then put that over 1.

Hope this helps!

By completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.

(a) To plot the lines y = 2x + 1 and y = 10 - x, we need to complete the tables of values and then plot the points on the axes.

For the line y = 2x + 1, we can choose some values of x and calculate the corresponding y values:

x | y

0 | 1

1 | 3

2 | 5

For the line y = 10 - x, we can also choose some values of x and calculate the corresponding y values:

x | y

0 | 10

1 | 9

2 | 8

Plot the points (0, 1), (1, 3), and (2, 5) for the line y = 2x + 1, and the points (0, 10), (1, 9), and (2, 8) for the line y = 10 - x on the provided axes.

(b) To find the solution to the simultaneous equations y = 2x + 1 and y = 10 - x,

we need to identify the point(s) where the two lines intersect on the graph.

From the plotted lines, we can see that they intersect at the point (3, 7). Therefore, the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7.

In conclusion, by completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.

For similar question on simultaneous equations.

https://brainly.com/question/148035  

#SPJ8

Answer:

Step-by-step explanation:

Answer:

The volume of the cylinder is 628.318530718

Step-by-step explanation:

The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.

The radius is 5, and the height is 8. Plug these values into the equation and solve:

[tex]v =\pi *5^2*8[/tex]

[tex]v = 628.318530718[/tex]

So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32

Answer:

200π or 628

Step-by-step explanation:

Note: your picture is not clear so I am assuming the height to be 8.

r = 5

h = 8

Volume = πr²h

= π * 5² * 8

= (25*8) π

= 200π

= 200*3.14

= 628

Answer:

Step-by-step explanation:

If bobby bought 5 books for 215.15 and they all cost the same, all you need to do is divide 215.15 by 5.

215.15/5=43.03

The answer to this problem is 43.03.

Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

Answer: 2011 and 2012

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

you add the hats to get the total number of hats then divide the answer by

No, it is much too high. Then the correct option is B.

An equation is a statement of equality between two expressions consisting of variables and/or numbers.

Given the question above, we need to find if the hats is to high or low.

Calculating the total numbers of hats made, we have

[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]

If Edna wants to split 62 hats evenly between two hospital, then each hospital will get

[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]

Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available

Hence, the correct option is B.

Learn more on equations at:

https://brainly.com/question/29657983

Edna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?

A. Yes

B. No, it is much too high

C. No, it is much too low

Answer:

B. 7

Step-by-step explanation:

3/KL = 12/28

KL = 3/(12/28) = (28 x 3)/12 = 7

       Hence,  The solution is:  

        x   =     1

        y   =  - 2

        z   =     2

Step-by-step explanation:

        3x  +  y  =  1

        x  -  y  +  z  =  5

        3x  +  y  +  z  =  3

        x  +  y  =  -1

        x  +  y  =   -1

        3x  +  y  =  1

        x   =   1

        y  =  -2

        1   -  (-2)  +   z    =   5

        z    =   2

       Hence, The Solution is:   x  =  1,   y  =  -2,    z   =  2

I hope this helps you!

Answer:

(- 7, 4 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

P (- 7, - 4 ) → (- 7, - (- 4) ) → (- 7, 4 )

Answer:

2, 4, 10, 20, 50, and 100.

Step-by-step explanation:

We would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.

To prove that triangles ΔXYZ and ΔFEG are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria, we need to show that they share certain corresponding angles and sides.

In ASA, we would need to show that both triangles have two congruent angles and the included side between those angles is congruent. In AAS, we would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.

Additional information that could be used to prove the congruence of ΔXYZ and ΔFEG using ASA or AAS includes:

1. Angle X = Angle F: If we can show that angle X in triangle ΔXYZ is congruent to angle F in triangle ΔFEG, we have one angle congruence.

2. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence.

3. Side XY = Side FE: If we can prove that side XY in triangle ΔXYZ is congruent to side FE in triangle ΔFEG, we have the included side congruence.

Alternatively:

4. Angle Z = Angle G: If we can show that angle Z in triangle ΔXYZ is congruent to angle G in triangle ΔFEG, we have the second angle congruence in AAS.

5. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence in AAS.

6. Side XZ = Side FG: If we can prove that side XZ in triangle ΔXYZ is congruent to side FG in triangle ΔFEG, we have a pair of non-included side congruence.

By establishing these angle and side congruences, we can use either the ASA or AAS congruence criteria to prove that triangles ΔXYZ and ΔFEG are congruent.

for more such question on triangle  visit

https://brainly.com/question/1058720

#SPJ8

The point (2, 7π / 2) does not belong to the implicit curve 8 · x · y + π · sin y = 55π and tangent and normal lines cannot be determined.

In this question we find the definition of an implicit curve, in which we must determine if point (2, 7π / 2) belongs to the curve. First, we check that point:

8 · x · y + π · sin y = 55π

8 · 2 · (7π / 2) + π · sin (7π / 2) = 55π

56π + 0.191π = 55π

56.191π = 55π

56.191 = 55 (CRASH!)

To learn more implicit curves: https://brainly.com/question/33483779

#SPJ1

33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)

To calculate the volume of a triangular prism, the formula that should be used is given as follows;

Volume= BH

where;

B= area of base = 1/2 × base×height

= 1/2×4×3

= 6

H= 6

Volume= 6×6= 36.

Learn more about volume here:

https://brainly.com/question/28795033

#SPJ1

Answer:

A) [tex]y-7=\frac{3}{4}(x+1)[/tex]

Step-by-step explanation:

[tex]y-y_1=m(x-x_1)\\y-7=\frac{3}{4}(x-(-1))\\y-7=\frac{3}{4}(x+1)[/tex]

Parallel lines must have the same slope, and then plugging in [tex](x_1,y_1)=(-1,7)[/tex], we easily get our equation.

Answer:

the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.

Step-by-step explanation:

To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 3/4.

Using the point-slope form of a line, which is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line, we can substitute the values (-1, 7) for (x₁, y₁) and 3/4 for m:

y - 7 = (3/4)(x - (-1))

Simplifying further:

y - 7 = (3/4)(x + 1)

Multiplying through by 4 to eliminate the fraction:

4(y - 7) = 3(x + 1)

Expanding:

4y - 28 = 3x + 3

Rearranging the equation to put it in standard form:

3x - 4y = -31

So, the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.

0.225 can be expressed as the fraction  1/200.

To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).

Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.

Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).

Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).

Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).

Therefore, 0.225 can be expressed as the fraction 1/200.

For more such questions on fraction, click on:

https://brainly.com/question/17220365

#SPJ8

Answer:

B) 1/2

Step-by-step explanation:

Note that pi=180.

Then we have 180/3=60 and so 5*60=300.

Thus cos 300=1/2.

Therefore, cos 5pi/3=1/2.

Answer: B

Step-by-step explanation:

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

For more such questions on tax charged visit:

https://brainly.com/question/1592982

#SPJ8

The interval for the graphed function that has a local minimum of 0 is [-2, 0].

To determine the interval for the graphed function that has a local minimum of 0, we need to examine the behavior of the graph around the x-values where it crosses the x-axis.

We know that the graph crosses the x-axis at -2.5, 0, and 3. Since the local minimum occurs at 0, we need to find the interval where the graph is decreasing to the left of 0 and increasing to the right of 0.

From the given information, we can determine the following:

The graph is decreasing between -2.5 and 0 because it crosses the x-axis at -2.5 and 0, and the minimum value is at (-1.56, -6).

The graph is increasing between 0 and 3 because it crosses the x-axis at 3, and the maximum value is at (1.2, 2.9).

The correct option is [–2, 0].

for such more question on interval

https://brainly.com/question/2141785

#SPJ8

Question

On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [2, 4]

By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.

Step-by-step explanation:

a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are two points on the line.

Using the altitude and temperature values provided:

(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),

we can calculate the slope:

m = (67 - 79) / (6400 - 4800)

= -12 / 1600

= -0.0075.

Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:

79 = (-0.0075)(4800) + b.

Solving for b, we have:

b = 79 + 0.0075(4800)

= 79 + 36

= 115.

Therefore, the linear model is T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) To find T(5800), we can substitute x = 5800 into the linear model:

T(5800) = -0.0075(5800) + 115

= -43.5 + 115

= 71.5.

Answers:

a) T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) 71.5 degrees.

a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.

b. The residual for this cycle is 2.07 minutes.

c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.

d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

e. No, the value of the y-intercept doesn't have meaning in the context of the problem.

Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:

ÿ = 33.35 + 13.29x

Part a.

When x = 4 minutes, the value of is given by:

ÿ = 33.35 + 13.29(4)

ÿ = 86.51 minutes.

Part b.

The residual for the given cycle can be calculated as follows;

Residual = y - ÿ

Residual = 62 - (33.35 + 13.29(2))

Residual = 62 - 59.93

Residual = 2.07 minutes.

Part c.

Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.

Part d.

The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

Part e.

In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.

Read more on regression here: brainly.com/question/16793283

#SPJ1

The shape is represented as below

The figure is of three shapes, the firs two are whole numbers then the last is a fraction.

Adding them results to

shape 1 + shape 2 + shape 3

1 + 1 + 1/4

As one fraction

= 9/4

as a mixed number

= 2 1/4

Learn more about fractions at

https://brainly.com/question/78672

#SPJ1

The measure of the indicated arc angle is 134 degrees.

The angle subtended by the arc at the centre of the circle is the angle of the arc.

Therefore, the central angle of an arc is the angle at the centre of the circle between the two radii subtended by the arc.

Hence, the central angle is also known as the arc's angular distance.

Therefore, the measure of an arc is the measure of its central angle.

Hence, the measure of the indicated arc is 134 degrees.

learn more on arc angle here: brainly.com/question/30194223

#SPJ1

The number of CDs Ahmed has: The expression (1/2) * c + 5 represents the number of CDs Ahmed has, as we derived earlier. Therefore, this option is correct. Option A

According to the given information, Ahmed has five more CDs than one-half the number of CDs Julia has. One-half of the number of CDs Julia has can be represented as (1/2) * c. Ahmed has five more CDs than this value, so we can express the number of CDs Ahmed has as:

Ahmed's CDs = (1/2) * c + 5

Now, let's analyze the options provided:

A. The number of CDs Ahmed has:

The expression (1/2) * c + 5 represents the number of CDs Ahmed has, as we derived earlier. Therefore, this option is correct.

B. The number of CDs Julia has:

The expression (1/2) * c + 5 does not directly represent the number of CDs Julia has. It represents the number of CDs Ahmed has. Therefore, this option is incorrect.

C. The number of CDs Ahmed has more than Julia:

This option is incorrect because the expression (1/2) * c + 5 represents the absolute number of CDs Ahmed has, not the difference between the number of CDs Ahmed and Julia have.

D. The number of CDs Ahmed and Julia have altogether:

The expression (1/2) * c + 5 represents only the number of CDs Ahmed has. It does not include Julia's CDs. Therefore, this option is incorrect.

In conclusion, the expression (1/2) * c + 5 represents the number of CDs Ahmed has.

For more such questions on number visit:

https://brainly.com/question/24644930

#SPJ8

Answer:

bob

Step-by-step explanation:

Answer:

Blank A:  (17, 0)

Blank B:  (-2, 19)

Step-by-step explanation:

Blank A:

Step 1:  Find the slope of AB:

Before we can find the equation of CD, we'll first need to find the slope of AB

We can do this using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where

Thus, we can plug in (-10, -3) for (x1, y1) and (7, 14) for (x2, y2) in the slope formula to find m, the slope of AB:

m = (14 - (-3)) / (7 - (-10))

m = (14 + 3) / (7 + 10)

m = 17 / 17

m = 1

Thus, the slope of AB is 1.

Step 2:  Find the slope of CD:

The slope of perpendicular lines are negative reciprocals of each other as shown by the following formula:

m2 = -1 / m1, where

Thus, we can plug in 1 for m1 in the perpendicular slope formula to find m2, the slope of CD:

m2 = -1 / 1

m2 = -1

Thus, the slope of CD is -1.

Step 3:  Find the y-intercept of CD:

One of the equations we can use when looking for intercepts is the slope-intercept form of a line, whose general equation is given by:

y = mx + b, where

Thus, we can plug in (5, 12) for (x, y) and -1 for m to find b, the y-intercept of the line, allowing us to have the full equation in slope-intercept of CD:

12 = -1(5) + b

12 = -5 + b

17 = b

Thus, the equation of CD is y = -x + 17

For any x-intercept, the y-coordinate will always be 0 since the line is intersecting the x-axis.

Thus, we can find the x-coordinate of the x-intercept by plugging in 0 for y in y = -x + 17 and solving for x:

0 = -x + 17

-17 = -x

17 = x

Thus, the x-coordinate of the x-intercept of CD is 17.

Thus, the coordinates of the x-intercept of CD are (17, 0)

Blank B:

We can see that (-2, 19) lies on CD when we plug in (-2, 19) for (x, y) in y = -x + 17, as we get 19 on both sides of the equation when simplifying:

19 = -(-2) + 17

19 = 2 + 17

19 = 19

Thus, (-2, 19) lies on CD.

The ray or segment that is a chord is (d) segment FC

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

The circle

By definition, a chord is a straight line that joins points of the circle without passing through the center

The ray that has the above properties is ray FC

Hence, the segments that is a chord is (d) FC

Read more about circle at

https://brainly.com/question/32192505

#SPJ1