A rectangular pyramid is sliced so the cross section is perpendicular to its base and passes through its vertex. What is the shape of the cross section? trapezoid rectangle triangle square

Answer:

4x-8+4y

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = - 2x² + 4x - 2

To find the y- intercept set x = 0

f(0) = 0 + 0 - 2 = - 2 ← y- intercept

The equation of the axis of symmetry is of the form x = c

where c is the value of the x- coordinate the line goes through.

Given the equation in standard form

with a = - 2, b = 4 then the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1

Equation of axis of symmetry is x = 1

Answer:

The y-intercept is -2

The equation of the axis of symmetry is x = 1

Step-by-step explanation:

* Lets revise the general form of the quadratic function

- The general form of the quadratic function is f(x) = ax² + bx + c,

 where a, b , c are constant

# a is the coefficient of x²

# b is the coefficient of x

# c is the y-intercept

- The meaning of y-intercept is the graph of the function intersects

 the y-axis at point (0 , c)

- The axis of symmetry of the function is a vertical line

  (parallel to the y-axis) and passing through the vertex of the curve

- We can find the vertex (h , k) of the curve from a and b, where

 h is the x-coordinate of the vertex and k is the y-coordinate of it

# h = -b/a and k = f(h)

- The equation of any vertical line is x = constant

- The axis of symmetry of the quadratic function passing through

  the vertex then its equation is x = h

* Now lets solve the problem

∵ f(x) = -2x² + 4x - 2

∴ a = -2 , b = 4 , c = -2

∵ The y-intercept is c

∴ The y-intercept is -2

∵ h = -b/2a

∴ h = -4/2(-2) = -4/-4 = 1

∴ The equation of the axis of symmetry is x = 1

Answer:

1. The number zero (0) is the additive identity for real numbers as adding it to any real number doesn't change the number.

2. a(b+c) = ab + ac or a(b-c) = ab-ac is the distributive property as a is distributed to b and then c.

3. An Equation with more than one variables is called literal equation. The variables are known in literal equations. These kind of equations are usually used to represent time, distance etc.

4. The number 1 is the multiplicative identity for real numbers as multiplying any real number with 1, other than zero, doesn't change the number.

5. The reciprocal of a number such that x is a number other than zero and 1/x is the reciprocal and the product of x and 1/x is equal to 1 then 1/x is called the multiplicative inverse of x.

Step-by-step explanation:

For a parabola y = ax² + bx + c, the vertex occurs at x = -b / (2a).

For f(x), a = -2, b = 0, and c = 9.  So the vertex is at:

x = -0 / (2×-2)

x = 0

At x=0:

f(0) = -2(0)² + 9

f(0) = 9

The maximum of g(x) is at 11.

So g(x) has a greater maximum value than f(x).

Final answer:

To convert 134.7 grams to milligrams, multiply by the conversion factor of 1000, resulting in 134700 milligrams.

Explanation:

To complete the statement 134.7 g = blank mg, one needs to understand the conversion between grams and milligrams. There are 1000 milligrams (mg) in 1 gram (g). When converting from a larger unit to a smaller unit, we multiply by the conversion factor. Therefore, multiplying 134.7 g by 1000 gives us the equivalent number of milligrams.

134.7 g × 1000 = 134700 mg

Thus, 134.7 g is equal to 134700 mg.

Answer:

fish 1 dollar

castle 6 dollars

Step-by-step explanation:

4x + y = 10

4x + 2y = 16

Multiply the first equation by -1

- 4x - y = -10

4x + 2y = 16

------------------------

0x  +y   = 6

y = 6

This means the castle costs 6 dollars

Substitute this into the first equation

4x+y =10

4x+6=10

Subtract 6 from each side

4x+6-6=10-6

4x=4

Divide by 4

4x/4=4/4

x=1

This means each fish costs 1 dollar

So x=1 the answer is 1

Answer:

Option B. 5P5 × 20P15

Step-by-step explanation:

It is very important to remember that the second grade students are sitting in the front row, therefore, it is only necessary to organize 15 first grade students in 20 seats.

Permutations allow you to calculate the number of ways in which m objects can be arranged in n positions.

The permutation of m in n is written as:

nPm

Where n is the number of elements and m are chosen.

The way in which the 5 second grade students can be organized in the 5 seats is from the first row is:

5P5

Then, the number of ways in which 15 first-year students can be organized into 20 seats is:

20P15

Then, the number of ways to organize all students on the bus is the product of both permutations

5P5 * 20P15

Answer:

0.61

Step-by-step explanation:

The average rate of change of H(s) in the closed interval [ a, b ] is

[tex]\frac{H(b)-H(a)}{b-a}[/tex]

here [ a, b ] = [ 80, 100 ]

H(b) = H(100)

= 0.003 × 100² + 0.07 × 100 - 0.027

= 30 + 7 - 0.027 = 36.973

H(a) = H(80)

= 0.003 × 80² + 0.07 × 80 - 0.027

= 19.2 + 5.6 - 0.027 = 24.773

Hence

average rate of change = [tex]\frac{36.973-24.773}{100-80}[/tex] = [tex]\frac{12.2}{20}[/tex] = 0.61

Answer:

Step-by-step explanation:

Lateral Area:

We have five congruent triangles with base = 7in and height h = 9in.

The formula of an area of a triangle:

[tex]A_triangle=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_\triangle=\dfrac{(7)(9)}{2}=\dfrac{63}{2}=31.5\ in^2[/tex]

The Lateral Area:

[tex]L.A.=5A_\triangle\to L.A.=5\cdot31.5=157.5\ in^2[/tex]

Surface Area:

S.A. = L.A. + B

L.A. - lateral area

B - area of a base

The base is the regular pentagon. The formula of an area:

[tex]B=\dfrac{a^2}{4}\sqrt{25+10\sqrt5}\approx1.72048a^2[/tex]

Substitute a = 7in:

[tex]B\approx1.72048(7^2)=84.303552\ in^2\approx84.3\ in^2[/tex]

The Surface Area:

[tex]S.A.=157.5+84.3=241.8\ in^2[/tex]

Answer:

9:00 P.M.

Step-by-step explanation:

All 3 bells ring at 9AM

1st bell: every 2 hours:

9AM, 11AM, 1PM, 3PM, 5PM, 7PM, 9PM

2nd bell: very 3 hours:

9AM, 12AM, 3PM, 6PM, 9PM

3rd bell: every 4 hours:

9AM, 1PM, 5PM,  9PM

So All 3 bells will ring at 9PM again

Answer:

the answer is that they will all ring at 9:00 pm

Step-by-step explanation:

9am=2, 3, 4

10am=0

11am= 2

12pm=3

1pm=2, 4

2pm= 0

3pm=3, 2

4pm= 0

5pm= 2, 4

6pm= 3

7pm=2

8pm= 0

9pm=2, 3, 4

Answer:

this is the Answer

Answer:

2.07%

Step-by-step explanation:

92 out of a total of 3,204 graduates earned a professional degree.  That works out to 0.0207, or 2.07%.

B) 2.87% of students earned a professional degree in 2009, calculated by dividing the number of professional degree holders by the total number of students.

To find the percentage of students earning a professional degree, divide the number of students with a professional degree (92) by the total number of students (3,204) and multiply by 100:

[tex]\[ \frac{92}{3,204} \times 100 \approx 2.87\% \][/tex]

Therefore, the correct answer is B) 2.87%.

Answer:

(-2, -3)

Step-by-step explanation:

2x + 1 = 3x + 3

minus 3 from both sides

2x - 2  = 3x

minus 2x from both sides

-2 = x

then plug in -2 for x

y = 2(-2) + 1

y = -4 + 1

y = -3

(-2, -3).

Step-by-step explanation:

Because the length of ST is calculated using pythagorean theorem:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

Where the square of the hypotenuse is equal to the sum of squares of the other two sides of a right triangle. In this case, the hypotenuse is ST and the other two sides are distances between S and T over the X and Y axis. Those are easily calculated:

[tex]x = |sx - tx| \\ y = |sy - ty| [/tex]

Where x is the distance between S and T over X axis and Y distance over Y axis, sx and tx are X coordinates of S and T, sy and ty are Y coordinates of S and T.

Using that formula, you get that y = 17 and x = 8.

Back to the pythagorean theorem, if we put those number in the formula of the pythagorean theorem, we get something like this:

[tex] {c}^{2} = {x}^{2} + {y}^{2} \\ {c}^{2} = {8}^{2} + {17}^{2} = 64 + 289 \\ {c}^{2} = 353 \\ c = \sqrt{353} [/tex]

And finally, the correct answer is in fact 353.

Answer:

central

Step-by-step explanation:

we know that

A central angle is an angle that forms when two radii are drawn from the center of a circle out to its circumference

so

A central angle has the same measure as its arc

The answer is 27 i think..

This triangle is a right triangle.

We know that the sum of the angles is 180°.

So:

90° + (x+23)°+ (x+13)° = 180°

90 + (x+23) + (x+13) = 180

(x+23)+(x+13) = 180-90

(2x+36) = 90

(2x) = 90-36

(2x) = 54

x = (54/2)

x = 27

=> x = 27

Check the picture below.

5+4+10+9+14 = 42.

Answer:

Hi, this question is a little unclear.  If you want to know what percentage he saved, it would be 30%, and to convert that percentage into a decimal would be a decimal of 0.30

Answer:

$70.00

Step-by-step explanation:

Add .00 to the end of each amount.

Make sure that the decimal points are lined up like a straight line.

Subtract 100.00 - 30.00

You should receive 70.00 and don't forget the dollar sign at the end so the answer is $70.00.

First Option

Triangles are are similar if we can turn one into the other by moving, rotating, flipping, or scaling. To solve this problem, we just need to match the ratios of the triangles. For both triangles we need to take the Change in y over the change in x, so:

[tex]\frac{change \ in \ y}{Change \ in \x}=\frac{y-b}{x-0}=\frac{m+b-b}{1-0} \\ \\ y-b=mx \\ \\ \boxed{y=mx+b}[/tex]

As you can see, this is the Slope-Intercept form of the equation of a line, where:

[tex]m: \ slope \\ \\ b: \ y-intercept[/tex]

Answer:

The first option would be the answer i believe

Step-by-step explanation:

Answer:

(B) The employee subtracted the wrong percent's.

Answer:

b she substracted wrong

Step-by-step explanation:

Answer:

2 eggs and 6 ounces of flour.

Step-by-step explanation:

To calculate this, we have to find 1/3 of 6 eggs and 18 ounces of flour separately.

So to calculate 1/3 of 6 eggs, multiply 6 by 1/3, which is to say divide 6 by(reciprocal) .Then you get 2 eggs.

Then similarly to calculate 1/3 of 18 ounces of flour, multiply 18 by 1/3, or divide it by 3. Then you get 6 ounces of flour.

So your answer is 2 eggs and 6 ounces of flour.

:)

Answer:

3u+15

Step-by-step explanation:

6u-3u

4+11

3u+15

Answer:

3u+15

Step-by-step explanation:

6u-3u +4+11

3u + 15

Answer:

C) 1/4,3/8,2/5

Step-by-step explanation:

First of all, let's rewrite all the fractions listed as decimal numbers:

[tex]\frac{2}{5}=0.400[/tex]

[tex]\frac{1}{4}=0.250[/tex]

[tex]\frac{3}{8}=0.375[/tex]

So the correct order from least to greatest should be

0.250, 0.375, 0.400

Which corresponds in fractional form to

1/4, 3/8, 2/5

So the correct option is

C) 1/4,3/8,2/5

The correct set of fractions ordered from least to greatest is C) 1/4, 3/8, 2/5.

To determine the set of fractions ordered from least to greatest, we need to compare them by finding a common denominator or converting them to decimals.

Let's convert the fractions to decimals:

Next, we order the decimals from smallest to largest:

Therefore, the correct order from least to greatest is: C) 1/4, 3/8, 2/5.

Answer:

9x^(3/2)=9 √(x^3 )  

Step-by-step explanation:

We are given

9x^(3/2)

We have to write the expression in radical form, for that the power has to be a multiple of ½

=9x^(3*1/2)

As we can see now the power is a multiple of 1/2. ½ will convert to square root while 3 will become the power of radicand.

So, 9 will remain outside of the square root while x will be inside the square root while having power 3.

=9 √(x^3 )

Hence,

9x^(3/2)=9 √(x^3 )  

Answer:

b. you're welcome

Step-by-step explanation:

If we want to share the money in equal parts, we have to consider that Eli has 9 shares, Freda has 13 shares and Geoff has 18 shares. So, in total, we have to split the money in

[tex]9+13+18 = 40[/tex]

parts. So, each part is

[tex]\dfrac{800}{40} = \dfrac{80}{4} = 20[/tex]£

Now, we distribute the shares:

Answer:

Eli gets £180

Freda gets £260

Geoff gets £360

Step-by-step explanation:

First, you need to make a ratio comparing their ages.

9 : 13 : 18 which is Eli : Freda : Geoff

Next, you need to work out the sum their ages (9+13+18) which is 40.

Then you divide the £800 (the amount that is being shared) by the sum of their ages 800÷40 which gives £20.And finally you need to multiply 20 by each section of the ratio.

So, 9×20 : 13×20 : 18 ×20 but then you need to simplify to get 180: 260 : 360.

Sorry if this explanation is confusing.

Answer:

Step-by-step explanation:Knowing that

There are 26 black cards and 26 red ones. Face card consists of jack (J), queen (Q), king (K). There are (26-6)=20 non face red cards. “Either ... or ...” here means bundle of both kinds of cards.

So, there are (26+20)=46 expected cards.

If you also ask for the probability, so the probability of the question asking above is equal to

23/26

Answer:

No there cannot be the same number of stickers on each page.

Step-by-step explanation:

If you want to find out how many stickers need to be in every page to be even you would add all the stickers up. 6+6+9+10+11= 42. Take the 42 and divide it by 5 to see how many stickers would go in each page. This will give you 8.4. However since this number is a decimal it can't be split evenly in whole stickers for each page. Meaning that it wouldn't be possible for each page to have a evenly distributed number of stickers per each page.

Answer:

x = 25

Step-by-step explanation:

4x+50 and 150 are vertical angles which means they are equal.

4x+50 =150

Subtract 50 from each side

4x+50-50 = 150-50

4x = 100

Divide each side by 4

4x/4 = 100/4

x = 25

Answer:

Option D. [tex]150\°[/tex]

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

[tex]m\angle ABC=\frac{1}{2}[arc\ ADC-arc\ AC][/tex]

substitute the given values

[tex]30\°=\frac{1}{2}[210\°-arc\ AC][/tex]

[tex]60\°=[210\°-arc\ AC][/tex]

[tex]arc\ AC=210\°-60\°=150\°[/tex]

Answer:

Option (D) is correct.

Step-by-step explanation:

OA is perpendicular to AB

OC is perpendicular to BC

Radius from the center is perpendicular to the tangent.

In quadrilateral ABCO,

∠ABC+∠BCO+∠AOC+∠OAB=360°

30°+90°+∠AOC+90°=360°

∠AOC+210°=360°

∠AOC=360°-210°

∠AOC=150°

Hence, arc AC=150°

Thus, the correct answer is option (D)

Answer:

There is no solution for this equation. :)

Please mark as brainliest!! :)