In which figure is point G an orthocenter? Triangle A B C is a right triangle. Lines are drawn from each point to the opposite side and intersect at point G. Triangle F D E is shown. Lines are drawn from each point to the opposite side and intersect at point G. The lines cut each side into 2 equal parts. Triangle L M N is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each angle has a different measure. Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G

The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100

An equation is an expression that shows the relationship between two or more variables and numbers.

The cost of each spoon is $8, hence A = 8. The cost of painting is 10, hence B = 10. Joshua can spend at most 100$, C = 100

8x + 10 ≤ 100

x ≤ 11.25

The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100

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Answer:

92 spoons can be purchased.

Step-by-step explanation:

10x + 8 ≤ 100

10x + 8 ≤ 100

8 - 8 10x 100 - 8

10x ≤ 92

x = 1/5

10 x 1/5 = 92.

<---------------------------------------------------------------------------------------------------------->

 <----------------------------------------------------0---------------------------- 92

Answer:

$72 would be the retail price

Step-by-step explanation:

Answer:

I'm not so sure of 7 and 8. but for number 9 we have to do 10*10= 100 The solution is D

Answer:

1436.026667 cubic yd

Step-by-step explanation:

given :

radius = 7 yards

pie = 3.14

we have ,

Volume of sphere = 4/3 × pie × r

=4/3 × 3.14 × 7

=1436.026667 cubic yards

Answer:

see explanation

Step-by-step explanation:

given that V is directly proportional to u and inversely proportional to f , then the equation relating them is

V = \(\frac{ku}{f}\) ← k is the constant of proportion

(a)

to find k use the condition when u = 1 and f = 3 , V = \(\frac{1}{6}\) , then

\(\frac{1}{6}\) = \(\frac{k}{3}\) ( cross- multiply )

6k = 3 ( divide both sides by 6 )

k = \(\frac{3}{6}\) = \(\frac{1}{2}\)

V = \(\frac{u}{2f}\) ← equation of proportion

(b)

when f = 4 and V = 1 \(\frac{1}{4}\) = \(\frac{5}{4}\) , then

\(\frac{5}{4}\) = \(\frac{u}{2(4)}\) = \(\frac{u}{8}\) ( cross- multiply )

4u = 40 ( divide both sides by 4 )

u = 10

Answer:

Simplify the matrix.

2√5=3=3,31,1,−3.5

Step-by-step explanation:

Answer:

The 90% confidence interval for the proportion of blocks that are sufficiently strong is (0.849, 1).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Twenty six of the 28 blocks were sufficiently strong.

This means that \(n = 28, \pi = \frac{26}{28} = 0.929\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.929 - 1.645\sqrt{\frac{0.929*0.071}{28}} = 0.849\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.929 + 1.645\sqrt{\frac{0.929*0.071}{28}} = 1.009\)

Since a proportion cannot be above 1, the upper limit is 1.

The 90% confidence interval for the proportion of blocks that are sufficiently strong is (0.849, 1).

The required linear equation is 25 + 5.75 x = y

A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given : A science museum

which charges $25 for the membership

And the charge for per visit is $ 5.75

Let y indicate the total cost and the number of visits be expressed by the variable x

thus the given equation is :

25 + 5.75 x = y

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Answer: x = -1 or x = 5/3

Step-by-step explanation:

|3x - 1| = 4

=> 3x - 1 = 4 or 3x - 1 = -4

=>x = 5/3 or x = -1

Answer:

The cost for 1 chair is $2.75 and the cost for 1 table is $8.75

Step-by-step explanation:

Use the elimination method of linear equations to find your answer.

Our equations for this problem are:

3c+5t=52 and 9c+7t=86

1. Multiply the entire first equation by -3.

-3(3c+5t=52)

2. Simplify the equation from above:

-9c-15t=-156

3. Stack the two equations on top of each other and add/subtract:

-9c-15t=-156

9c+7t=86

4. You should be left with -8t=-70. Simplify this to find the value of t:

t=8.75

5. Plug the value of t into any of the original equations and solve for c.

3c+5(8.75)=52

6. Simplify the equation above:

3c+43.75=52

7. Subtract 43.75 from both sides of the equation:

3c=8.25

8. Divide both sides by 3 to get your c value:

c=2.75

The measure of second angle and third angle of the isosceles triangle will be equal to 69° each.

What is an isosceles triangle ?

An isosceles triangle is a triangle which has two equal sides and two equal angles.

It is given that the first angle of an isosceles triangle is 42°. In a triangle sum of all angles is equal to 180°.

We know that in an isosceles triangle the measure of two angles and two sides are equal.

The measure of first angle is 42°. Let's assume the measure of second angle is x this meant the measure of third angle will be x too.

∵ Sum of three angles of a triangle = 180°

∴ 42 ° + ( x + x ) = 180°

or

42 ° + ( 2x ) = 180°

2x = 180° - 42°

2x = 138°

or

x = 69°

As measure of both unknown angles is same , so second angle and third angle will have a measure of 69° each.

Therefore , the measure of second angle and third angle of the isosceles triangle will be equal to 69° each.

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7x²+5x​

(9x²+8x)-(2x²+3x)

We will subtract the like terms. That means that we will subtract \(2x^{2}\) from \(9x^{2}\) and 3x from 8x.

Answer:

The rectangle is 7 cm x 18 cm

Step-by-step explanation:

w = width

l = length

(1)  A = wl = 126 cm²

(2) P = 2w + 2l = 50 cm

Solve equation (2) for w:

2w = 50 - 2l

w = (50 - 2l) / 2 = 25 - l         plug this in to equation (1)

(25 - l)(l) = 126

-l² + 25l - 126

Use quadratic formula to find the 2 roots of l:  a = -1, b = 25. c = -126

l = 7, 18

Since l > w, then l = 18

Solve for w:

w = 126/18 = 7

The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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Answer:

D

Step-by-step explanation:

When x = 1, y = 5

When x = 3, y = 15

So, using this, find the slope.

(15 - 5) / (3 - 1) = 10 / 2 = 5

For every x, y increases by 5.

So, y = 5x, or D

Answer:

D

Step-by-step explanation:

5x

you need help

nice for you                                                                                                                                   / fyi this is payback

Answer:

30 square units

Step-by-step explanation:

10 (height) x 6 (base) / 2 =

60 / 2 =

30 square units

Hope that helps!

Answer:

50k

Step-by-step explanation:

The volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis is 2π[e - e^1 + 1]   and the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis is πtan^2(1).

1) To find the volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis, we can use the method of cylindrical shells.

First, let's express the equation in terms of x: x = ln(y)/y. Now we can set up the integral to calculate the volume. The volume can be obtained by integrating the product of the circumference of each cylindrical shell and its height over the interval [0, 1]:

V = ∫[0,1] 2πx(e^x) dx.

Using integration by parts, we can evaluate this integral as follows:

V = 2π ∫[0,1] x(e^x) dx

 = 2π [x(e^x) - ∫[0,1] e^x dx]

 = 2π [x(e^x) - e^x] | [0,1]

 = 2π[(1(e^1) - e^1) - (0(e^0) - e^0)]

 = 2π[e - e^1 + 1].

2) To find the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis, we can again use the method of cylindrical shells.

Let's express the equation in terms of x: x = tan(y). Now we can set up the integral to calculate the volume. The volume can be obtained by integrating the product of the circumference of each cylindrical shell and its height over the interval [0, 1]:

V = ∫[0,1] 2πtan(y) dy.

Using the substitution method, we can evaluate this integral as follows:

Let u = tan(y), then du = sec^2(y) dy.

When y = 0, x = tan(0) = 0, and when y = 1, x = tan(1).

Now, the integral becomes:

V = 2π ∫[0,1] u du

 = 2π [u^2/2] | [0,1]

 = 2π[(tan(1))^2/2 - 0]

 = πtan^2(1).

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Answer:

8 becaus it dives. 2 meters second so if it dives to meters every second then all you have to do is add to to 4 seconds

The equivalent ratios are 8: 6 and 12:9.    

Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.  

Here we have 4:3

To find equivalent ratios, we can multiply both terms by the same number.

Multiplying by 2

=> 4 × 2 : 3 × 2

=> 8 : 6

Multiplying by 3

=> 4 × 3 : 3 × 3

=> 12: 9

Therefore,

The equivalent ratios are 8: 6 and 12:9.    

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Complete Question

What is the equivalent ratio for 4: 3

Answer:

S8 is 64

Step-by-step explanation:

\({ \boxed{ \bf{S_{n} = \frac{n}{2} [2a + (n - 1)d]}}}\)

n is number of terms; n = 8

a is the first term; a = 1

d is the common difference: d = 3-1; d = 2

\({ \sf{S_{8} = \frac{8}{2}[(2 \times 1) + (8 - 1) \times 2 ]}} \\ \\ { \sf{{S_{8}} = 4(2 + 14)}} \\ { \sf{S_{8}}} = 4 \times 16 \\ { \sf{S_{8}}} = 64\)

Missy will need a minimum of 570 square inches of wrapping paper to completely cover the box.

To calculate the minimum amount of wrapping paper needed to cover the box, we need to find the surface area of the box.

A rectangular box has six sides: a top, a bottom, two sides, and two ends.

The top and bottom sides have the same dimensions, which are 17.5 inches by 10 inches. So each of these sides has an area of 17.5 in × 10 in = 175 square inches.

The two side surfaces also have the same dimensions, which are 17.5 inches by 4 inches.

Each of these sides has an area of 17.5 in × 4 in = 70 square inches.

The two end surfaces have the same dimensions, which are 10 inches by 4 inches. Each of these sides has an area of 10 in × 4 in = 40 square inches.

To find the total surface area of the box, we add up the areas of all six sides:

175 in² (top) + 175 in² (bottom) + 70 in² (side 1) + 70 in² (side 2) + 40 in² (end 1) + 40 in² (end 2)

Total surface area = 570 in².

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Answer:

B

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , so

∠ c + 56° + 38° = 180°

∠ c + 94° = 180° ( subtract 94° from both sides )

∠ c = 86°

Answer:

47

Step-by-step explanation:

Add all the numbers together in order to receive the total number of 8th grade students.