Simplify this expression:
4(1 - 3x) + 7 x - 8

Step-by-step explanation:

Hello, there!!!

Let's simply work with it,

Firslty let's assume the whole cake, when you assume the cake in whole. you get,

length (l)= 16 in

breadth (d)= 6 in

and height (h)= 4 in

now, as it is a rectangle shaped cake,

volume of a whole cake (v)= l×b×h

or, v= 16 in × 6 in × 4 in.

Therefore, the volume of whole cake is 384 cubic inch.

now,

let's find the volume of eaten part,

As per the picture, the 1/4th part of cake is eaten so,

length = 8 in

breadth = 3in

and height = 4in.

so, volume of eaten part = l × b × h

v= 8in × 3in × 4in

Therefore , v= 96 cubic inch.

now, lastly finding the volume of remaining part,

v. of remaining part = v.of whole cake - v. of eaten part.

or, v. of remaining part = 384 in^3 - 96 in^3

Therefore, the volume of remaining part is 288in^3.

Hope it helps....

Answer:

Step-by-step explanation:

Ok so I go to the store

I spend X/2 - 10 and I'm left with x/2

Then I got to store 2 and spend x/2 - 10 again and now have no money left.

So

x/2-10=0

x/2=10

x=20

Before that, she had:

x/2-10=20

x/2=30

x=60

So she started out with $60

She has $60, to begin with when she went to the first store.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs arithmetic operations is called an arithmetic operator.

Operators let do basic mathematical calculations.

+ Addition operation: Adds values on either side of the operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

For example 4 + 2 = 6

Let she had x money before the second store.,

So x-x/2–10=0 => x = 20.

Let she had y money before the first store,

where x = y-y/2–10.

So y/2 = 20+10=30

⇒ y = 60

Hence, she has $60, to begin with when she went to the first store.

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Answer:

See below

Step-by-step explanation:

Quarters= 25(x)

Nickels =5(x+16)

25x+5(x+16)=590 (no decimal)

If you solve for x, you’ll get the number of quarters.

Answer:

d = p + 85

Step-by-step explanation:

We don't have a lot to go on for this problem. We have two undefined variables.

In order to solve for d, we need to isolate it:

d - 85 = p

Add 85 to both sides

d = p + 85

Answer:

YZ = 8.5

Step-by-step explanation:

Since RY is an angle bisector then the ratio of the sides of the triangle are equal to the corresponding ratio of the base, that is

[tex]\frac{YX}{YZ}[/tex] = [tex]\frac{XR}{ZR}[/tex] , substitute values

[tex]\frac{11.9}{YZ}[/tex] = [tex]\frac{7}{5}[/tex] ( cross- multiply )

7YZ = 59.5 ( divide both sides by 7 )

YZ = 8.5

Answer:

a) 7b+6=97

b)b=13

Step-by-step explanation:

Total cost = $97

Cost of each book = $7

Cost of shipping =$6

Therefore ,

Cost of the total no. of books+ Cost of shipping = Total Cost

=>7b+6= 97   <------- Answer to part(a)

=>7b=97-6

=>7b=91

=>b=13

No. of books = 13 <--------- Part (b)

Answer:

F(8,6)

Step-by-step explanation:

(x₁,x₂)  --> E (-7, 2)

F(x₂,y₂)

Midpoint M(0.5 , 4)

Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{+y_{1}+y_{2}}{2})[/tex]

[tex](\frac{-7+x_{2}}{2},\frac{2+y_{2}}{2}) = (0.5, 4)\\\\[/tex]

Compare x,coordinates and y-coordinates,

[tex]\frac{-7+x_{2}}{2}= 0.5 \ ; \ \frac{2+y_{2}}{2}=4\\\\[/tex]

-7 + x₂ = 0.5*2    ; 2+y₂ = 4*2

-7+ x₂ = 1             ; 2 +y₂ = 8

     x₂ = 1+ 7        ;      y₂ = 8 - 2

     x₂ = 8            ;     y₂ = 6

F(8,6)

Answer:

F(8,6)

Step-by-step explanation:

(x₁,x₂)  --> E (-7, 2)

F(x₂,y₂)

Midpoint M(0.5 , 4)

Midpoint =

Compare x,coordinates and y-coordinates,

-7 + x₂ = 0.5*2    ; 2+y₂ = 4*2

-7+ x₂ = 1             ; 2 +y₂ = 8

    x₂ = 1+ 7        ;      y₂ = 8 - 2

    x₂ = 8            ;     y₂ = 6

F(8,6)

Answer:

The correct choice is option A. $31.95

Step-by-step explanation:

The total cost would be the basic fee + the price of the boxes.

So, the initial fee is $12, Joyce needs 5 boxes, and $3.99 is charged per box.

$12 + 5 × $3.99 = 31.95

Answer:

Surface area of the cone = 1306.24 square centimeters

Step-by-step explanation:

Surface area of a cone is determined from the formula,

Surface area of cone = πr(r + l)

where 'r' = radius of the circular base of the cone

l = lateral height of the cone

And π = 3.14

Surface area of the cone with 'r' = 13 cm and 'l' = 19 cm

Surface area = 3.14(13)(13 + 19)

                     = 3.14(13)(32)

                     = 1306.24 square centimeters

Answer:

5(2+2s)

= 10+10s

hope it helps <3

Answer:

5(2+2s)=10+10s

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Once you have two sides and the included angle, there is only one triangle.

Answer: 1

Answer:

The answer is B. 1

Step-by-step explanation:

I hope I helped

Answer:

23

Step-by-step explanation:

[tex]2 y + 7[/tex]

Replace y with 8

[tex]= 2 (8) + 7\\= 16+ 7\\= 23[/tex]

Therefore, the value of the expression when y=8 is 23.

I hope this helps!

Answer:

The equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is;

S + 429 = 85 × 6

Step-by-step explanation:

The parameters given are;

The scores earned by Mele on the first five test in Economics II are;

75, 70, 92, 95, and 97 points

The total test points = 429 points

Therefore, the score, S, Mele needs to earn on the 6th test for him to get an average of exactly 85 points for the 6 tests is found as follows;

From the definition of average, μ = (Sum of data values)/(Number of data)

Sum of data values = S + 429

The number of data = 5 test + 6th test =  6

μ = 85 = (S + 429)/6

Therefore;

S + 429 = 85 × 6

Therefore, the equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is S + 429 = 85 × 6.

The sample space of the probability experiment: shooting a free throw in basketball. is [tex]n(X)=2[/tex] from the calculations below

Sample space:In probability theory, the sample space (also called sample description space of an experiment or random trial is the set of all possible outcomes of the experiment.

Let

The sample space for a player shooting single free throws be equal to X

Let Scored free throws be A

And missed free throws be B

Generally the possible outcomes is mathematically given as

[tex]X=(A,B)[/tex]

Therefore

In conclusion the Sample space of the probability experiment of shooting a free throw in basketball is

[tex]n(X)=2[/tex]

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Answer: 31.39%

Step-by-step explanation:

Given: The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years.

i.e. [tex]\mu = 7 \ \ \ \ \sigma= 1.8[/tex]

Let X be the age of rocks in an isolated area .

Then, the probability that rocks are between 5.8 and 7.3 years old :

[tex]P(5.8<X<7.3)=P(\dfrac{5.8-7}{1.8}<\dfrac{X-\mu}{\sigma}<\dfrac{7.3-7}{1.8})\\\\=P(-0.667<Z<0.167)\ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<0.167)-P(z<-0.667)\\\\=P(Z<0.167)-(1-P(z<0.667))\\\\=0.5663-(1-0.7476)\\\\=0.3139[/tex]

[tex]=31.39\%[/tex]

Hence, the percent of rocks are between 5.8 and 7.3 years old = 31.39%

Step-by-step explanation:

Here,

diameter(d) of the cylinder is 16 yd.

radius of a cylinder is 16/2 yd= 8 yd.

height (h) of a cylinder is 18yd.

now, we use formula for surface area of cylinder,

a= 2.pi.r(r+h)

or, a= 2×3.14×8(8+18)

by simplifying it we get,

The surface area of cylinder is 1306.24 sq.yd.

Hope it helps...

Answer:

The surface area of this cylinder is:

1306.24 square yards

Step-by-step explanation:

  There are 2 types of surface:

then:

total  surface = 2 flat surface + circular surface

ts = 2(п r²) + (п*d*h)

ts = total suface

п ≈ 3.14

d = diameter = 16 yd

r = radius = diameter/2 = 16/2 = 8yd

h = high = 18yd

then:

ts = 2(3.14*8²) + (3.14*16*18)

ts = 2(3,14*64) + (904,32)

ts = 2(200.96) + 904.32

ts = 401.92 + 904.32

ts = 1306.24 yd²

Answer:

The lateral area of this square pyramid is 100 in^2

Step-by-step explanation:

The lateral area of a polyhedron is the added area of all lateral faces (faces on the side) excluding the bases.

In this case, the lateral sides of the square pyramid are the 4 triangular faces on the sides.

AREA OF ONE TRIANGULAR FACE (given by the formula 1/2 x bh):

1/2 x 10 x 5 = 25

Multiply that by 4 since all 4 triangular faces are similar:

25 x 4 = 100

So the lateral area of the square pyramid is 100 in^2.

Please rate my answer once you know its score! :DD

Answer:

Arc BC = 117°

Step-by-step explanation:

Angle D is an inscribed angle that intercepts arc ABC. According to the Inscribed angle theorem of a circle, m<D = ½ of arc ABC.

Thus,

104° = ½(AB + BC)

104° = ½(91° + BC)

Multiply both sides by 2

104*2 = 91 + BC

208 = 91 + BC

Subtract both sides by 91

208 - 91 = BC

117 = BC

Arc BC = 117°

Answer:

b

Step-by-step explanation:

Answer:

The answer is D or (10,-9)

Step-by-step explanation:

Since y is already given (and you have to use the substitution method) substitute y into one of the equations. So you should have something like this:

-2x+11=3x+21

After that merely solve for x which should get you x=10. After you get your x value plug 10 in either (of the original) equation and your y value should be -9. For example if you chose y=-2x+11 you should have y= -2(10)+11. In the end your answer should be (10,-9).

If you want to check your work merely plug your answer into both equations (ex: -9=-2(10)+11 --> -9=-9), therefore you know your answer is correct).

Hope this helped!

It follows from the definition of the derivative and basic properties of arithmetic. Let f(x) and g(x) be functions. Their derivatives, if the following limits exist, are

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h\text{ and }g'(x)\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]

The derivative of f(x) + g(x) is then

[tex]\displaystyle \big(f(x)+g(x)\big)' = \lim_{h\to0}\big(f(x)+g(x)\big) \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)+g(x+h)\big)-\big(f(x)+g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)-f(x)\big)+\big(g(x+h)-g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{f(x+h)-f(x)}h+\lim_{h\to0}\frac{g(x+h)-g(x)}h \\\\ \big(f(x)+g(x)\big)' = f'(x) + g'(x)[/tex]

2x+10=14

x=2

Area: 14.4= 56

3x+16=25

3x=9

x=3

17x-1,7=37,4

17x=39,1

x=2,3

Answer:

i think

third option is correct.

cosY = 8 / 17, cotY = 8 / 15, secY = 17 / 8 is the required trigonometric functions of the same angle. Option C is correct

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
cosY = 8 / 17, cotY = 8 / 15, secY = 17 / 8
Is the trigonometric function of the same angle,
cosY = 1 / SecY
8 / 17 = 1 / secY
secY = 17 / 8
Now,
P = √[17² - 8²]
P = 15
CotY = 8 / 15

Thus, trigonometric functions in option C are of the same angle.

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Answer:

Step-by-step explanation:

If the sides exist in a ratio to one another, then when you multiply some number x by both the length and the width, they still remain as a ratio. The length will be 3x and the width will be 1x. The perimeter formula is

P = 2L + 2W and since our perimeter is 72 and we have both the length and the width, we can fill in the formula and solve for x:

72 = 2(3x) + 2(1x) and

72 = 6x + 2x and

72 = 8x so

9 = x.

If x = 9, then 1x = 9 and 3x = 27. Let's check the perimeter against those side lengths.

P = 2(3x) + 2(1x) and

P = 2(27) + 2(9) and

P = 54 + 18 so

P = 72

and you're done! (The bold numbers above are the width and length, respectively.)

Answer:

20 gesse will fill the gap

Explanation:

We were told that the V forms a right angle which means the angle is at 90 degrees.

From trigonometry, for a right angle triangle we have the opposite, hypotenose and adjacent, then here the 12 side is the opposite and 16 sides is the adjacent, then the hypotenose will be the gap we are looking for using below expression

a²+ b²= c²

So,

12²+ 16²= c²

144 + 256 = c²

c=√(144 + 256)

c = √400

c=20

Therefore, 20 gesse will fly in the missing gap of the V formation.

CHECK THE ATTACHMENT FOR THE TRIANGLE

BEST OF LUCK

Answer:

(-1,3)

Step-by-step explanation:

Using midpoint formula, we have

x=(-4+2)/2=-1

y=(-2+8)/2=3

The point shown on g(x) is (1,3)

If x = 1 and y = 3, this means x is multiplied by 3 ( 1 x 3 = 3)

This makes g(x) 3x^2

The answer is A.