Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.

A solid right pyramid with a square base has a base edge measuring 6 inches.

Which is the slant height of the pyramid if Helen uses all the clay?

3 inches
4 inches
5 inches
6 inches

Answer:

x = 45

Step-by-step explanation:

5 (2x - 5) = 1/2 (18x + 40)​

10x - 25 = 9x + 20

10x = 9x + 45

x = 45

please mark this answer as brainlist

Answer:

[tex]\frac{a+3}{6}[/tex]

Step-by-step explanation:

Treat it like any other math problem with a equals sign:

6x + 3 = a

subtract 3 from both sides: 6x = a + 3

divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]

swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]

the only time the sign flips is if you divide by a negative

Step-by-step explanation:

x^2+2x+7y=15

7y=15-x^2-2x

y=15/7-1/7x^2-2/7x , x ∈ all real numbers

Answer:

1. The discount is 10%

2. 250

Answer:

Step-by-step explanation:

The 15 cm by 15 cm piece of cardboard area = 225 cm².

A cube has six congruent faces. If each edge is 5 cm, the surface area is 6×5² = 150 cm². So there is enough cardboard to make a cube, but not by folding. You'd have to do some cutting and taping.

Answer:

12x - 28° = 116°

7x + 32° = 116°

Step-by-step explanation:

12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.

Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:

12x - 28° = 7x + 32°

Collect like terms

12x - 7x = 28 + 32

5x = 60

Divide both sides by 5

5x/5 = 60/5

x = 12

✔️12x - 28°

Plug in the value of x

12(12) - 28

= 144 - 28

= 116°

✔️7x + 32°

7(12) + 32

= 84 + 32

= 116°

Answer:

√65

Step-by-step explanation:

(-6,4) (-5,-4)

√(x2 - x1)² + (y2 - y1)²

√[-5 - (-6)]² + (-4 - 4)²

√(1)² + (-8)²

√1 + 64

√65

Answer:

90 ml of the 25 percent mixture and 585 of pure alcohol

Step-by-step explanation:

Firstly, you should find the quantity of alcohol in the desired mixture.

675:100*90= 675*0.9= 607.5

Firstly,  define all the 25 percents mixure as x, the pure alcohol weight is y.

1. x+y= 675 (because the first and the second liquid form a desired liquid).

Then find the equation for spirit

The first mixture contains 25 percents. It is x/100*25= 0.25x

When the second one consists of pure alcohol, it contains 100 percents of spirit,  so it is x.

2. 0.25x+y=607.5

Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)

try 2-1 to get rid of y

x+y- (0.25x+y)= 675-607.5

0.75x= 67.5

x= 90

y= 675-x= 675-90= 585

It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol

Answer:

-1

Step-by-step explanation:

f(x) = x²+3x+1

f(a) = a²+3a+1

f'(a) = 2a+3

putting a = -2

2×(-2)+3

= -4+3

= -1

Answer:

[tex]-\frac{x^{2} }{4}[/tex]  -2x - 7

Step-by-step explanation:

Never seen a phone with 3 cameras before or something but ok.

Took a while to use brainly's insert character thingie since fractions and the exponent kinda threw me off.

Answer:

Slope is B. ¼

Step-by-step explanation:

Slope: is hypotenuse

[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]

Answer:

50

Step-by-step explanation:

So we know that 42/3=14.

3 years before was:

14-3=11

42-3=39

The sum of 11+39 is 50

Answer:

[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]

Step-by-step explanation:

[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]

Answer:

B

Step-by-step explanation:

[tex]\\ \sf\longmapsto \left\{x|x \epsilon I,x\leqslant 3\right\}[/tex]

In listing

[tex]\\ \sf\longmapsto \left\{\dots,0,1,2,3\right\}[/tex]

Answer:

52.8

Step-by-step explanation:

(3×2.6×2/2)+(3×5×3)

= 7.8+45

= 52.8

Answered by GAUTHMATH

9514 1404 393

Answer:

 3, 6, 12, 24

Step-by-step explanation:

It helps if the formula is properly written.

 Tn = a·r^(n-1)

Fill in the given values for a, r, and use n = 1 to 4.

 T1 = 3·2^(1-1) = 3

 T2 = 3·2^(2-1) = 6

 T3 = 3·2^(3 -1) = 12

 T4 = 3·2^(4 -1) = 24

__

Additional comment

The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.

 3, 6, 12, 24, ...

Answer:

1,-3,-5

Step-by-step explanation:

Given:

f(x)=x^3+7x^2+7x-15

Finding all the possible rational zeros of f(x)

p= ±1,±3,±5,±15 (factors of coefficient of last term)

q=±1(factors of coefficient of leading term)

p/q=±1,±3,±5,±15

Now finding the rational zeros using rational root theorem

f(p/q)

f(1)=1+7+7-15

  =0

f(-1)= -1 +7-7-15

    = -16

f(3)=27+7(9)+21-15

   =96

f(-3)= (-3)^3+7(-3)^2+7(-3)-15

    = 0

f(5)=5^3+7(5)^2+7(5)-15

   =320

f(-5)=(-5)^3+7(-5)^2+7(-5)-15

     =0    

f(15)=(15)^3+7(15)^2+7(15)-15

    =5040

f(-15)=(-15)^3+7(-15)^2+7(-15)-15

     =-1920

Hence the rational roots are 1,-3,-5 !

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

The critical value used is [tex]T_c = 2.132[/tex]

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 5 - 1 = 4

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357

The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Step-by-step explanation:

Step 1:  Factor the equation

[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]

Step 2:  Find the x-intercepts of the graph of f(x)

[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]

[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]

Step 3:  Describe the end behavior of the graph of f(x)

Since the function is to the power of 2, that means that it is a parabola.  And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.

Step 4:  What are the steps you would use to graph f(x)

The first step that I would do is factor the equation.  Then I would find the x-intercepts of the graph and plot them on the graph.  I would then plug in 0 for all of the x values to get the y intercept.  After doing that I would get the vertex using the vertex formula plotting it on the graph.  Finally, I would connect all of the dots together to form the graph of the equation.

Answer:

The person above me is correct!

Answer:

Hello,

Are you still alive ?

Step-by-step explanation:

a)

c=k*b (c varies directly as b)

6=k*2 ==> k=3 ( c = 6 when b = 2.)

[tex]\boxed{c=3*b }\\[/tex]

b)

b=14 ==> c=3*14=42

c)

c=39

[tex]b=\dfrac{c}{3} =\dfrac{39}{3} =13\\[/tex]

9514 1404 393

Answer:

  20th

Step-by-step explanation:

The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.

20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.

The 20th person will receive all gifts.

_____

The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.

  2 = 2¹

  4 = 2²

  5 = 5¹

LCM(2, 4 5) = 2² × 5¹ = 20

Answer:

undefined, invalid

and for a limit expression like a/x, x->0 we also say this is infinite.

9514 1404 393

Answer:

Step-by-step explanation:

The 1-year interest is simply the invested amount times the interest rate.

Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...

  1400r + 900(r +.02) = 202

  2300r +18 = 202 . . . . . . . . . .simplify

  2300r = 184 . . . . . . . . . .subtract 18

  r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r

$1400 was invested at 8%.

$900 was invested at 10%.

Answer:

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]

Step-by-step explanation:

Given

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]

Required

Simplify

We have:

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]

Open brackets

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]

Collect like terms

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]

Answer:

138 yards

Step-by-step explanation:

1 feet is (1/3) yard

414 feet is (1/3)*414=138 yards

Answer:

Let the number be x

According to Question ,

2x + 3x = 40

5x = 40

x = 8

therefore , the number is 8

hope that helps uh...☺