Carl, Caitlyn, and Daryl are comparing their ages. Carl is two years older than Caitlyn. Daryl is five years older than Carl. The product of Carl and Daryl's ages is at least 160. If x represents Caitlyn's age, which inequality represents this situation?

Answer:

I'm going to go with B.

Step-by-step explanation:

but don't just take my answer bc I'm not 100% sure

The given figure is an example of an Orthographic drawing.

So the correct option is option D.

In  Orthographic drawing, we represent several 2D views of an object to obtain a 2D object.

The most common views of Orthographic drawings are top, right, and front.

Though the figure mentioned in the question represents the top, right, and front part view and as per the definition of perspective drawing it is not flat,  it cant be looked flat when opened which satisfies the definition of net so, the figure satisfies option 3.

Thus, the figure is an example of an Orthographic drawing.

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Answer:

6 ounces

Step-by-step explanation:

4 tablespoons 1/4 cup 2 fluid ounces

5 1/3 tablespoons 1/3 cup 2.7 fluid ounces

8 tablespoons 1/2 cup 4 fluid ounces

12 tablespoons 3/4 cup 6 fluid ounces

The solution is 6 fluid ounces

The value of 3/4 cups of water is given by the equation A = 6 fluid ounces

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 amount of water be represented as A

Let the number of cups of water be = 3/4 cups

Now ,

1/4 cups = 4 tablespoons = 2 fluid ounces

1/2 cups = 8 tablespoons = 4 fluid ounces

So , 3/4 = ( 1/2 ) + ( 1/4 )

And , Substituting the values in the equation , we get

3/4 cups = 12 tablespoons = 6 fluid ounces

Therefore , the value of A is 6 fluid ounces

Hence , the equation is A = 6 fluid ounces

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Answer: 6 hours as lifeguard 8 hours as cashier.

Step-by-step explanation: 6x13=78 11x8=88 78+88/166

Answer: C

Step-by-step explanation:

6+3=9

9+3=2

Answer: A

Step-by-step explanation:

6+3=9

9+3=12

Answer:

47/4  or 11.75 = m

Step-by-step explanation:

-47 -2.5 = -2.5 - 1.7m - 2.3m

Combine like terms

-49.5 = -2.5 -4m

Add 2.5 to each side

-49.5 +2.5 = -2.5+2.5 -4m

-47 = -4m

Divide each side by -4

-47/-4 = -4m/-4

47/4 = m

11.75 = m

Answer:

1. [tex] \boxed{ \bold{ \sf{ - 3x + 5}}}[/tex]

2. [tex] \boxed{ \bold{ \sf{ {x}^{4} + 3 {x}^{3} + 2x}}}[/tex]

Step-by-step explanation:

1. [tex] \sf{(2x + 2) + (3 - 5x)}[/tex]

When there is a ( + ) in front of expression in parentheses , the expression remains the same.

⇒[tex] \sf{2x + 2 + 3 - 5x}[/tex]

Collect like terms

⇒[tex] \sf{ - 3x + 2 + 3}[/tex]

Add the numbers

⇒[tex] \sf{ - 3x + 5}[/tex]

2. [tex] \sf{( {3x}^{3} - 4 {x}^{4} ) + (2x + 5 {x}^{4}) }[/tex]

When there is a ( + ) in front of expression in parantheses , the expression remains the same

⇒[tex] \sf{3 {x}^{3} - 4 {x}^{4} + 2x + {5x}^{4} }[/tex]

Collect like terms

⇒[tex] \sf{ {x}^{4} + 3 {x}^{3} + 2x}[/tex]

Hope I helped!

Best regards!!

Answer: 40

Step-by-step explanation:

angle 1 and 2 are alternative interior angle which means they are equal

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

angle 1= angle 2

2x+20=3x+10

      x=10

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

angle 1=2x+20

           =2(10)+20

           =20+20

           =40

Step-by-step explanation:

Hey there!!

Just do it in a simple way.

Use the properties of parallel lines, and find the value of x to find angke 1.

angle 1= angle 2 { alternate angles on parallel lines are equal }

[tex]2x + 20°= 3x + 10°[/tex]

or, 3x-2x = 20°-10°

x= 10°.

now,

angle 1= 2x+ 20°

=2×10°+20°

Therefore, the measure os angle 1 is 40°.

Hope it helps...

Answer:

3km = 3000000 milimeters = 3000000mm

Step-by-step explanation:

1 km = 1000 meters

1 meter = 1000 milimeters

then:

1km = 1000*1000 = 100000 milimiters = 1000000mm

3km = 3*1000000 = 3000000 milimeters

Answer:

The number of 7-digit numbers are possible in a single area code is 5248600

Step-by-step explanation:

The given parameters are;

The number of digits in the area code = 7

The possible digits for X, B and C are 1 - 9 = 9 digits

The number of possible digits for A is 0 - 9 = 10 digits

Exceptions

1) B and C cannot both =

2) 555-0100 through 555-0199 are reserved for television or movies

Therefore, we have, the number of 7 digits numbers without exceptions = 10×9⁶ = 5314410 numbers

The number of the exceptions are

Exception 1) 10 × 1 × 1 × 9 × 9 × 9 × 9 = 65610 numbers

Exception 2)  555-0100 through 555-0199 = 0199 - 0100 = 200 numbers

The number of possible numbers = 5314410 - 65610 - 200 = 5248600

The number of 7-digit numbers are possible in a single area code = 5248600.

Answer:

x^2-2x-8

Step-by-step explanation:

FOIL the two together and get x^2 for the first, -4x outer, +2x inner, -8 last. Then combine like terms and get x^2-2x-8

Answer:

(fg)(x)) = x² - 2x -8

Step-by-step explanation:

----------

Answer:

[tex]\large \boxed{\mathrm{(a) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(b) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(c) \ All \ real \ numbers}}[/tex]

Step-by-step explanation:

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

Expand brackets.

2x+4x-4=2+4x

Combine like terms.

6x-4=2+4x

Subtract 4x from both sides.

Add 4 to both sides.

2x=6

Divide both sides by 2.

x=3 (One solution)

25-x=15-(3x+10)

Distribute negative sign.

25-x=15-3x-10

25-x=-3x+5

Add x and -5 to both sides.

20=-2x

Divide both sides by -2.

-10=x (One solution)

4x=2x+2x+5(x-x)

Solve for brackets.

4x=2x+2x+5(0)

4x=2x+2x

Combine like terms.

4x=4x

Divide both sides by 4.

x=x

All real numbers are solutions. (All real numbers)

Answer:

greater

39 million>107

The solution is 39 million is greater than 10⁷

The value 3.9 x 10⁷ is greater than the value 10⁷

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 equation be represented as A

Now , the value of A is

A = 39 million

Let the value of B = 10⁷

On simplifying the value of A , we get

A = 39 million

A = 39000000

So , the value A can be written in powers of 10 as

The value of A = 39 x 10⁶

On simplifying the equation , we get

The value of A = 3.9 x 10⁷

Now , the value of A > B

And , 3.9 x 10⁷ > 10⁷

Therefore , the value of A is greater than B

Hence , The value 3.9 x 10⁷ is greater than the value 10⁷

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Answer:

-262

Step-by-step explanation:

Given sequence is: 33, 28, 23, 18...

First term a = 33

Common Difference d = 28 - 33 = - 5

To find: [tex] t_{60}[/tex]

By nth term of an AP.

[tex]t_n = a + (n - 1)d \\ t_{60} = 33 + (60- 1)( - 5) \\ t_{60} = 33 + 59( - 5) \\ t_{60} = 33 - 295\\ t_{60} = - 262\\ [/tex]

Answer:

P=(a+b)*2

P=(2x+8+5x-2)*2=(7x+6)*2=14x+12

Step-by-step explanation:

perimeter is the distance round. Add all the algebras

2x+8+5x-2+2x+8+5x-2

{combine the like terms}

P= 14x+12

Answer:

34000cm or 340m

Step-by-step explanation:

We have to find total surface area.

dimensions of 1 wooden box =

l = 1m = 100cm

b = 80cm

h = 25cm

∴ In the case of 2 =

l = 100cm

b= 80cm

h  = 25 + 25 = 50cm

T.S.A = 2(lb + lh + bh)

= 2(100*80 + 100*50+ 80*50)

= 2(8000+5000+4000)

= 2*17000

= 34000cm

= 340m

Answer: [tex]1\dfrac{29}{60}\text{ minutes}[/tex]

Step-by-step explanation:

Given: A total eclipse solar eclipse in 2003 lasted [tex]5\dfrac{3}{20}[/tex] minutes

[tex]=\dfrac{5(20)+3}{20}=\dfrac{103}{20}\text{ minutes}[/tex]

& a total eclipse solar eclipse in 2005 lasted [tex]3\dfrac{2}{3}[/tex]minutes

[tex]=\dfrac{3(3)+2}{3}=\dfrac{11}{3}\text{ minutes}[/tex]

Difference= [tex]\dfrac{103}{20}-\dfrac{11}{3}=\dfrac{103\times3-11\times20}{60}[/tex]

[tex]=\dfrac{309-220}{60}\\\\=\dfrac{89}{60}\text{ minutes}\\\\=1\dfrac{29}{60}\text{ minutes}[/tex]

So, 2003 solar eclipse was [tex]1\dfrac{29}{60}\text{ minutes}[/tex] longer than solar eclipse in 2005.

Answer:

i dont know this man if i did  would help

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

n = 2

Answer:

Approximate marks sally get = 95%

Step-by-step explanation:

Given:

Sally's study time = 1.5 hour = 1.5 × 60 = 90 minute

Find:

Approximate marks sally get.

Computation:

Number of minute sally study = 1.5 × 60

Number of minute sally study = 90 minutes

Using graph,

Vertical line on 90 minutes shows 95% , we can say that the person who study 90 minutes per day get 95% marks

So,

Approximate marks sally get = 95%

Answer:95

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

The computation of the other integer is shown below:

The Factor of 48 is 2^4 × 3

Also the greatest common divisor is 24,

This results that the second number also contains the factors 2^3 and 3 but not a fourth 2.

Now when there is a division of 240 by 48 so the number comes is 5

Now the second number factors are 2^3 and 3 that represents that it is under the factors of 48 but the factor 5 would arise from the second number

So, the other number is 120

Answer:

120

Step-by-step explanation:

If you want the aops explanation:

The prime factorization of 48 is $2^4\cdot3$. Since the greatest common factor is 24, that means the other number also has the factors $2^3$ and 3 but not a fourth 2. When we divide 240 by 48, we get 5. The factors $2^3$ and 3 of the other number are covered by the factors of 48, but the factor 5 must come from the other number. So, the other number is $2^3\cdot3\cdot5=\boxed{120}$.

Answer:

To make AB perpendicular to CD move point B until the angle between the lines, BEC measures 90°.

Step-by-step explanation:

Plato

If you have to make AB perpendicular to CD, rotate AB clockwise, until and unless both the lines intersect at 90 degrees.

Angles : the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.   

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is that as you move point B, the angle formed between AB and CD varies.

If you have to make AB perpendicular to CD, rotate AB clockwise, such that the point B moves in clockwise direction, until and unless both the lines intersect at 90 degrees.

Therefore, if you have to make AB perpendicular to CD, rotate AB clockwise, until and unless both the lines intersect at 90 degrees.

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Greetings from Brasil...

Let's find the equivalent fractions

A/B ; C/D  ⇔  A·D/B·D ; C·B/B·D

Bringing to our problem:

A/B ; C/D  ⇔  A·D/B·D ; C·B/B·D

1/3 ; 2/5  ⇔  1·5/3·5 ; 2·3/3·5  ⇔  5/15 ; 6/15

Now we can sum/add the equivalent fractions

5/15 + 6/15 = 11/15

11/15   to accomodation and food

15/15 = total

total - (accomodation and food) = other purposes

15/15 - 11/15 = 4/15

So 4/15 its the fraction for other purposes

Answer:

Point B

Step-by-step explanation:

The square root of 11 is about 3.31. SO the most accurate point is B.

Answer: the rules are

+(+) Two like signs become a positive sign

−(−) 6−(−3) = 6 + 3 = 9

+(−) Two unlike signs become a negative sign

−(+)

Step-by-step explanation:

Example:  3+(+2) = 3 + 2 = 5, 6−(−3) = 6 + 3 = 9, 7+(−2) = 7 − 2 = 5,8−(+2) = 8 − 2 = 6  hope this helps you :)

Answer:

no solution

Step-by-step explanation:

2x - 3 > 2(x+9)

Distribute

2x-3 > 2x+18

Add 3 to each side

2x-3+3 > 2x+18+3

2x> 2x+21

Subtract 2x from each side

2x-2x> 2x-2x+21

0 > 21

This is never true so there is no solution

Answer:

See below.

Step-by-step explanation:

So we have the inequality:

[tex]2x-3>2(x+9)[/tex]

First, distribute the right side:

[tex]2x-3>2x+18[/tex]

Subtract both sides by 2x. Both the left and right cancels:

[tex](2x-3)-2x>(2x+18)-2x\\-3>18[/tex]

-3 is not greater than 18. Therefore, the inequality is never true.

Answer:

Rectangle 1 area: 53 units squared

Shape 2 area: 43.75 units squared

Step-by-step explanation:

Shape 1:

We need to find the area of the two triangles in this rectangle and subtract it from the total area of the rectangle.

Total area of the rectangle:

13 * 5 = 65

Area of triangles (they are congruent):

1/2 * 4 * 3 = 6

6 * 2 = 12

65 - 12 = 53

The area of the shaded part is 53 (I don't know what your unit of measurement is. Just say units.)

Shape 2:

First, let's find the area of the parallelogram at the top.

10 * 3 = 30

Now, let's find the area of the rest of the shape. Triangle first...

1/2 * 4 * 1.5 = 3

Now, the rectangle and the tiny triangle we can section out at the end:

7 * 1.5 = 10.5 + 1/4 (Triangle) or 0.25 = 10.75

Total area: 10.75 + 3 + 30 = 43.75

Answer:

The algebraic expression is:

a + 5 = 7

Step-by-step explanation:

The algebraic expression is:

a + 5 = 7

then:

a = 7-5

a = 2

and the number is:

2

Answer:

(12, 2) 85° 95° 2.72 units 3.29 units

(11, 1) 81° 99° 2.03 units 3.04 units

(4, 2) 90° 90° 3.62 units 3.62 units

(8, 5) 102° 78° 5.70 units 4.37 units

(9, 7) 109° 71° 6.93 units 4.82 units

Step-by-step explanation:

I was looking for an answer then decided to do it myself and these are the correct answers.

(12, 2)

85° 95° 2.72 units & 3.3 units

(11, 1)

81° 99° 2.03 units & 3.04 units

(4, 2)

90° 90° 3.62 units & 3.6 units

(8, 5)

102° 78° 5.70 units & 4.4 units

An ordered pair is a composition of the x-coordinate and the y-coordinate, having two values written in a fixed order. Ordered pair helps to locate a point on the Cartesian plane.

The cartesian plane is a two-dimensional coordinate plane, which is formed by the intersection of the x-axis & y-axis. The 2 axes intersect at the angle of 90degree to each other at the point called the origin.

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