As James bought his textbooks for classes one semester, he estimated the cost to the nearest ten dollars. He knew he could cover the cost up to $315. His math book cost $68.41, biology text was $105.35, literature text cost $72.49, and the AutoCAD text was $59.91. What rounded sum did James determine

Answer:

First, subtract

7

from each side of the inequality to isolate the

x

term while keeping the inequality balanced:

1

4

x

+

7

−

7

>

0

−

7

1

4

x

+

0

>

−

7

1

4

x

>

−

7

Now, multiply each side of the inequality by

4

to solve for

x

while keeping the inequality balanced:

4

×

1

4

x

>

4

×

−

7

4

4

x

>

−

28

1

x

>

−

28

x

>

−

28

Answer:

1/2 < x < 7/2

Step-by-step explanation:

First, simplify then put everything on one side: 16x -4x^2 -7 > 0

Then use the quadratic formula to factor and find out x.

For a quadratic equation in the form of ax^2 + bx + c = 0, use this formula:

X (1,2) = (-b ± √(b^2 -4ac))/2a

(The X (1,2) part means that there are 2 solutions for x)

In this case, a is -4, b is 16, and c is -7. By using this formula, you get that x=1/2, x=7/2

Answer:

25%

Step-by-step explanation:

1 dozen = 12

3 out of 12

3/12

Simplify

1/4

Multiply top and bottom by 25 to get a denominator of 100

25/100

25%

Answer:

but what to do in do I have to find the area of the particular Region or a length of that

Answer:

1 : 45

Step-by-step explanation:

Given

Rs 20 and 900 ( divide both by 20 )

= 1 : 45

Answer:

[tex](a)\ Ratio = 13.5 : 4[/tex]

(b) The height of the smaller bucket is 10.7

Step-by-step explanation:

Given

[tex]V_L = 13\frac{1}{2}[/tex]

[tex]V_S = 4[/tex]

[tex]H_L = 36cm[/tex]

Solving (a): The ratios

This is represented as:

[tex]Ratio = V_L : V_S[/tex]

So, we have:

[tex]Ratio = 13\frac{1}{2} : 4[/tex]

Express as decimal

[tex]Ratio = 13.5 : 4[/tex]

Solving (b): The height of the smaller bucket

The ratio of the heights is:

[tex]Ratio = H_L : H_S[/tex]

So, we have:

[tex]13.5 : 4 = H_L : H_S[/tex]

Substitute known value

[tex]13.5 : 4 = 36 : H_S[/tex]

Express as fraction

[tex]4/13.5 = H_S/36[/tex]

Multiply by 36

[tex]36 * 4/13.5 = H_S[/tex]

[tex]10.7 = H_S[/tex]

[tex]H_S = 10.7[/tex]

Step-by-step explanation:

something is missing here.

it is not clear, what exactly is 27 km. only the side of the orange triangle ? or the whole distance to the 90 degree angle ?

but in both cases that is not enough. we need some information about the split ratio of the orange side and the white side. it some angles in the graphic.

otherwise I can simply keep the given sides with their lengths but freely move the line between the orange and white triangles. there are infinite many solutions.

is it meant to be an isoceles triangle (2 equal sides) ? it certainly does not look like it, but that would be the only case where the given information can lead to a solution.

under that assumption the baseline of the white triangle is also 27 km.

the first side is 9km.

the second side we get via Pythagoras :

27² = 9² + x²

729 = 81 + x²

648 = x²

x = 25.46 km

now, since this is a right-angled triangle we can (especially to calculate the area) also consider the two sides enclosing the 90 degree angle as baseline and height.

the area of a triangle is baseline×height/2

area = 9×25.46/2 = 114.55 km²

Your answer is -6.

Hope my answer is helpful to you. Stay blessed .

[tex]\\ \large\sf\longmapsto {27}^{x} = {9}^{x - 3} \\ \\ \large\sf\longmapsto ( {3}^{3} ) {}^{x} = ({3}^{2} ) {}^{x - 3} \\ \\ \large\sf\longmapsto 3 {}^{3x} = 3 {}^{2(x - 3)} \\ \\ \large\sf\longmapsto {3}^{3x} = 3 {}^{2x - 6} \\ \\ \large\sf\longmapsto 3x = 2x - 6 \\ \\ \large\sf\longmapsto 3x - 2x = - 6 \\ \\ \large\sf\longmapsto x = - 6[/tex]

Answer:

9

Step-by-step explanation:

See the picture for steps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{1}{4} (38 -14) + \dfrac{3^3}{9}}[/tex]

[tex]\mathsf{38-14=\bf 24}[/tex]

[tex]\mathsf{= \ \dfrac{1}{4} (24)+\dfrac{3^3}{9}}[/tex]

[tex]\mathsf{\dfrac{1}{4}(24)= \bf 6}[/tex]

[tex]\mathsf{= \ 6+\dfrac{3^3}{9}}[/tex]

[tex]\mathsf{3^3}\\\mathsf{= 3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= \bf 27}[/tex]

[tex]\mathsf{= \ 6+\dfrac{27}{9}}[/tex]

[tex]\mathsf{\dfrac{27}{9}}\\\mathsf{= 27\div9}\\\mathsf{= \bf 3}[/tex]

[tex]\mathsf{= \ 6 + 3}[/tex]

[tex]\mathsf{= \bf 9}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf 9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

12

Step-by-step explanation:

vzhhhdhx

gxbdhd

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hjcjc

Answer:

Step-by-step explanation:

pi = 3.14

r = 11 yds

Formula

Area = 4 pi r^2

Solution

Area = 4 * 3.14 * 11 ^2

Area = 1519.76

Area = 1519.8 rounded to the nearest 1/10

Answer:

Use the equation y=mx+c

the slope(m) is 2,y is -7and x is 6

therefore you firstly have to find the y intercept (c)

y=mx+c

-7=2(6)+c

-7=12+c

-7-12=c

-19=c

then replace the gradient and y intercept in the equation

y=mx+c

y=2x-19

or you can use the formula y-y1= m( x-x1)

I hope this helps

Answer:

Step-by-step explanation:

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

Answ

Step-by-step explanation:

-2/2 =-1 nha

Answer:

17.6 mi

Step-by-step explanation:

I know you are using Windows 10 OS or something because of the cortana thingie and task bar option, and you can do Windows Key + Shift + S to take a screenshot.

This gives much better quality than a third party device and lets us evade the terrible pixel green line rippley thingies that form. Plus it is more efficient and faster.

Circumference formula is Diameter * Pi.

I assume the 5.6 mi. is the diameter since the line segment is going completely through the circle.

Pi is something of the lines of 3.141592653 blah blah blah and goes on forever, but the point is, we take it to be 3.14 when doing circle stuff so we don't die from old age trying to figure out a question of a 1 x 1 circle.

So 5.6 * 3.14 is 17.584 which is your answer.

It says to round to the nearest tenth though, so you round and get

17.6 since the 5 in 17.584 is the tenths place, the 8 is the hundredths place, the 4 is the thousandths place and so on and so forth.

(The "  *  " symbol represents multiplication and is in use all the time when going to higher levels of education.)

Answer: x+2y+6=0

Option 3

Explanation:

y = (-x-6)/2

2y = -x-6

x+2y+6=0

Must click thanks and mark brainliest

Answer:

the school band

Step-by-step explanation:

the band, the band has a percentage of 53.85...,which is (14/26)x100, and the choir has 35.71% which is (5/14)x100

[ (10)(x^3)(y^2) / (5)(x^-3)(y^4) ]^-3

[ (2)(x^3)(y^2) / (x^-3)(y^4) ]^-3

[ (2)(x^6)(y^2) / (y^4) }^-3

[ (2)(x^6)(y^-2) ]^-3

(2^-3)(x^-18)(y^6)

---Not simplified (contains negative exponents)

(1/8)(x^-18)(y^6)

---Fully simplified

(y^6) / (8)(x^18)

Hope this helps!

Answer:

I doubt it is not going to be a great

Step-by-step explanation:

the same time as a child support of the year old girl I don't know what you think about it is not going to

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then

[tex]3^{-2}[/tex] = [tex]\frac{1}{3^2}[/tex] = [tex]\frac{1}{9}[/tex]

Answer:

1.02secs

Step-by-step explanation:

Using the equation of motion

v = u+at

Since the ball moves upward then:

a = -g

Substitute into the formula

v = u-gt

Given the following

Initial velocity u = 10m/s

Final velocity v = 0m/s (on the ground)

g = 9.8m/s²

Required

Time t

Substitute the given values into the formula

0 = 10-9.8t

-9.8t = -10

t = 10/9.8

t = 1.02secs

Hence your opponent have 1.02secs

Answer:

7x and 2x. 3x^2 and -7x^2.

Step-by-step explanation:

7x and 2x both have x. 3x^2 and -7x^2 both have x^2.

Answer:

x = 35.0

Step-by-step explanation:

the height is 26√3 since the left one is a 30-60-90 triangle

so to find x

cos(39) = x/26√3

or, x = 26√3×cos(39)

or, x = 35.0

Answered by GAUTHMATH

Answer:

c = 85 yd

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

c² = 77² + 36² = 5929 + 1296 = 7225 ( take square root of both sides )

c = [tex]\sqrt{7225}[/tex] = 85

Answer:

[tex]85yd[/tex]

Step-by-step explanation:

According to PYTHAGORAS Theorem,

[tex] {c}^{2} = {77}^{2} + {36}^{2} \\ {c}^{2} = 5929 + 1296 \\ {c}^{2} = 7225 \\ c = \sqrt{7225} \\ c= 85yd[/tex]

Answer:

3/2

Step-by-step explanation:

Let it be

C (5;4) , A (2;1) ; B(7;6)

Suppose that C divide the line AB in ratio m/n from point A (AC is m, CB is n)

Use the formula xc=(m*xb+n*xa)/ (m+n)

5=(m*7+2n)/(m+n)

5m+5n= 7m+2n

2m=3n

m/n=3/2

Answer:

again it has a ratio

Step-by-step explanation:

follow this steps.

firstly look at the side and you got the ratio 24/16

secondly write 42/? and multiply by 24/16

the answer is ?*24=42*16 and divide it by 8 and write again ?*3=42*2 and finally the answer is ?=28

f(x)=3x²+x-3x-1

=x(3x+1)-(3x+1)

=(x-1)(3x+1)

Answer:

12 starfish

Step-by-step explanation:

Create a system of equations where x is the number of starfish he has and y is the number of spiders he has:

x + y = 19

5x + 8y = 116

Solve by elimination by multiplying the top equation by -8:

-8x - 8y = -152

5x + 8y = 116

Add these together and solve for x:

-3x = -36

x = 12

So, he has 12 starfish.

The total number of starfish is 12 starfishes

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of starfish be = x

Let the number of spiders be = y

The number of legs for spiders = 8

The number of legs for starfish = 5

So , the equation will be

The total number of legs for x starfish = 5x

The total number of legs for y spiders = 8y

The total number of creatures = 19

So , x + y = 19   be equation (1)

And ,

The total number of legs = 116

So , 5x + 8y = 116   be equation (2)

Now , from equation (1) , x = 19 - y

Substituting the value of equation (1) in equation (2) , we get

5x + 8y = 116

5 ( 19 - y ) + 8y = 116

95 - 5y + 8y = 116

95 + 3y = 116

Subtracting 95 on both sides , we get

3y = 21

Divide by 3 on both sides , we get

y = 7

So , the number of spiders is 7 spiders

Substituting the value of y in equation (1) , we get

x + y = 19

x + 7 = 19

Subtract 7 on both sides , we get

x = 12

Therefore , the value of x is 12

Hence , The total number of starfish is 12 starfishes

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ2

Answer:

h=17.3 A=173

Step-by-step explanation:

Calculator

Answer:

height = 17.3 mm

area = 173 mm²

Step-by-step explanation:

all three sides are of the same length (20 mm).

so, the height actually splits the baseline in half

(2 × 10 mm) while hitting it at a 90 degree angle.

so, we use Pythagoras, where the full side opposite of this 90 degree angle is c (Hypotenuse), the height of the main triangle is one side, and half of the baseline is the other side.

c² = a² + b²

20² = 10² + height²

400 = 100 + height²

300 = height²

height = 17.3 mm

the area of the main triangle is baseline (20) times height divided by 2.

so,

At = 20×17.3/2 = 10×17.3 = 173 mm²

Answer:

[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]

Step-by-step explanation:

we would like to solve the following using double-angle formula:

[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]

there're 4 double Angle formulas of cos function which are given by:

[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]

since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore

step-1: assign variables

to do so rewrite the given function:

[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]

so,

Step-2: substitute:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]

recall unit circle thus cos300 is ½:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]

simplify square:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]

reduce fraction:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]

simplify substraction and hence,

[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]

The required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

The formula for calculating the volume of the conical lid's is expressed as

[tex]V = \frac{1}{3} \pi r^2h[/tex] where:

r is the radius

h is the height

v is the volume

Given the following

r = x

If the conical lid’s height is 2 centimeters less than the radius, x, then;

h = x - 2

V = 25π cm³

Substitute the given values into the formula as shown:

[tex]25 \pi = \frac{1}{3} \pi x^2 (x-2)\\3(25) = x^2(x-2)\\Expand\\75=x^3-2x^2\\Swap\\x^3-2x^2 = 75\\Equate \ to \ zero\\x^3-2x^2 - 75 = 0[/tex]

Hence the required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

Answer:

AC² + BD² = 2[AB² + BC²]

Step-by-step explanation:

Let the parallelogram be ABCD with sides AB, BC, CD and AD. It also has diagonals AC and BD.

Since the diagonals are perpendicular and bisect each other at their mid-point, and P is the point of intersection of the diagonals, we have that AP = AC/2, PC = AC/2, PB = BD/2 and PD = BD/2.

Since APB forms a right angled triangles with length of sides AP, PB and AB where AB is the hypotenuse side, using Pythagoras' theorem, we have

AB² = AP² + PB²

Since AP = AC/2 and PB = BD/2, we have

AB² = (AC/2)² + (BD/2)²

AB² = AC²/4 + BD²/4   (1)

Also, BPC forms a right angled triangles with length of sides BP, PC and BC where BC is the hypotenuse side, using Pythagoras' theorem, we have

BC² = BP² + PC²

Since PC = AC/2 and PB = BD/2, we have

BC² = (AC/2)² + (BD/2)²

BC² = AC²/4 + BD²/4   (2)

Adding equations (1) and (2), we have

AB² = AC²/4 + BD²/4   (1)

+

BC² = AC²/4 + BD²/4   (2)

AB² + BC² = AC²/4 + BD²/4 +  AC²/4 + BD²/4

AB² + BC² = AC²/2 + BD²/2

Multiplying through by 2, we have

2[AB² + BC²] = AC² + BD²

So, AC² + BD² = 2[AB² + BC²]  which proves our expression.

Answer:

B. 3ˣ + 8x + 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3ˣ + 10x

g(x) = 2x - 4

Step 2: Find

Answer:

3^x+8x+4

Step-by-step explanation:

f(x) = 3^x + 10x

g(x) = 2x - 4

(f- g)(x)=3^x + 10x  - (2x - 4)

Distribute the minus sign

(f- g)(x)=3^x + 10x  - 2x + 4

Combine like terms

         3^x+8x+4