The width of a rectangle is 8 cm less than its length. The diagonal of the rectangle is 12 cm.
Determine the dimensions of the rectangle. (4 marks)

Answer:

AM = 50

Step-by-step explanation:

12x + 8 = 10x + 15

subtract 10x from both sides

2x + 8 = 15

subtract 8 from both sides

2x = 7

divide both sides by 2

x = 3.5

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

AM = 12x + 8

AM = 12(3.5) + 8

AM = 42 + 8

AM = 50

Answer:

there should be 4 points below the trend line

Step-by-step explanation:

4

Answer:

[tex]y=-3x+4[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]6x+2y=2[/tex]

Rearrange this equation in slope-intercept form (so it's easier for us to identify the slope)

Subtract 6x from both sides to isolate 2y

[tex]6x+2y-6x=-6x+2\\2y=-6x+2[/tex]

Divide both sides by 2 to isolate y

[tex]y=-3x+1[/tex]

Now, we can tell clearly that -3 is in the place of m. Therefore, because parallel lines have the same slope, we know that the line we're solving for will also have a slope of -3. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-3x+b[/tex]

2) Determine the y-intercept

[tex]y=-3x+b[/tex]

Plug in the given point (-1,7)

[tex]7=-3(-1)+b\\7=3+b[/tex]

Subtract 3 from both sides

[tex]7-3=3+b-3\\4=b[/tex]

Therefore, the y-intercept of the line is 4. Plug this back into [tex]y=-3x+b[/tex]:

[tex]y=-3x+4[/tex]

I hope this helps!

Answer:

6

Step-by-step explanation:

the top and the bottom line on the squares and with the top and the bottom line on both of the arrows

The required number of lines of symmetry the given figure holds is 2.

A line of symmetry is a line that divides a shape into two mirror images that are identical to each other. If a shape has a line of symmetry, it means that one-half of the shape is a reflection of the other half across the line of symmetry.

For example, a square has four lines of symmetry, because it can be divided into four identical mirror images. A rectangle has two lines of symmetry, one horizontal and one vertical because it can be divided into two identical mirror images.

Following the above example, in the given scenario, the figure has only 2 lines of symmetry.

Learn more about the line of symmetry here:

https://brainly.com/question/30963765

#SPJ2

Answer:

4/7 = 8/14

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

[tex]\frac{4}{x} =\frac{8}{14} \\[/tex]

cross multiply

8x = 14 x 4

8x = 56

x = 7

Answer:

There are 6,840 possible outcomes for these awards.

Step-by-step explanation:

Given that a group of 20 people are going to run a race, and the top three runners earn gold, silver, and bronze medals, to determine how many outcomes are possible for these awards, the following calculation must be performed:

20 x 19 x 18 = X

380 x 18 = X

6.840 = X

Therefore, there are 6,840 possible outcomes for these awards.

Total outcomes that are possible for these awards are 6840 outcomes, calculated using permutation.

Total number of people=20

permutation means the arrangement of items while the combination is all about the selection of some out of many.

let us say start with the gold medal

no of ways a gold medal can be given = ²⁰C₁ = 20

Now, the number of people left is 19

no of ways a silver medal can be given = ¹⁹C₁ = 19

Now, the number of people left is 18

no of ways a bronze medal can be given = ¹⁸C₁ = 18

possibility of total outcomes=20*19*18 = 6840ways

Therefore, total outcomes that are possible for these awards=6840

to get more about permutations and combinations refer to the link,

https://brainly.com/question/4658834

Answer:

4

Step-by-step explanation:

Answer:

last one

Step-by-step explanation:

it has 15.95 and only 1 16.00 :D

Answer: [tex]19.31\ ft[/tex]

Step-by-step explanation:

Given

The tower is at a height of [tex]h=20\ ft[/tex]

the angle of depression is [tex]15^{\circ}[/tex]

Suppose the surfer is x ft away from the base of the tower

[tex]\therefore \text{From the figure, we can write}\\\\\Rightarrow \cos 15^{\circ}=\dfrac{x}{h}\\\\\Rightarrow x=h\cos 15^{\circ}\\\Rightarrow x=20\cos 15^{\circ}\\\Rightarrow x=19.31\ ft[/tex]

Therefore, the surfer is at a distance of 19.31 ft from the base of the tower.

Answer:

C) 24>x

Step-by-step explanation:

The inequality is just turned around. 24>x is thw same thing as x<24.

Hope this helped :)

Answer:

D

Step-by-step explanation:

x+3≥12

<=> x≥8

so 8 is less than x

x is less than 24 means 24>8 but in this case we must follow a model so x is less than 24 can be write 24≥x (read x is less than 24 or is equal to 24)

The ratio of red squares to blue squares is 3 : 7

The ratio of blue squares to total squares is 7 : 10

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion be represented as A

The number of red squares = 15

The number of blue squares = 35

Now , the total number of squares is N = 50 squares

a)

The ratio of red squares to blue squares is = number of red squares / number of blue squares

The ratio of red squares to blue squares is = 15 / 35

The ratio of red squares to blue squares is = 3 : 7

b)

The ratio of blue squares to total squares is = number of blue squares / total number of squares

The ratio of blue squares to total squares is = 7 : 10

Hence , the proportion is solved

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ3

The complete question is :

A quilt is made of 15 red squares and 35 blue squares. Find the ratio, in lowest terms of:

a) The ratio of red squares to blue squares

b) The ratio of blue squares to total squares

[tex]115 = l \times 2.5 \times 5.75[/tex]

[tex] \huge \mathrm{Answer࿐}[/tex]

given :

[tex]\longmapsto[/tex] volume = 115 yd³

Dimensions are :

We know,

[tex] \large \boxed{ \mathrm{volume = l \times b \times h}}[/tex]

Therefore Length of the prism is 8 yards.

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Answer:

No

Step-by-step explanation:

We need to tell that whether 8 satisfies the given inequality. The inequality is ,

[tex]:\implies[/tex] 48 < 4x

Putting x = 8

[tex]:\implies[/tex] 48 < 4x

[tex]:\implies[/tex] 48 < 4 * 8

[tex]:\implies[/tex] 48 < 32

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

[tex]\mathsf{48 < 4x}[/tex]

[tex]\large\textsf{TURN the given EQUATION}[/tex]

[tex]\mathsf{4x > 48}[/tex]

[tex]\large\textsf{DIVIDE 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{4x}{4}>\dfrac{48}{4}}[/tex]

[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{4}{4}}\large\textsf{ because that gives you 1}[/tex]

[tex]\large\textsf{KEEP: }\mathsf{\dfrac{48}{4}}\large\textsf{ because it helps us compare to the x value.}[/tex]

[tex]\mathsf{x >\dfrac{48}{4}}[/tex]

[tex]\mathsf{\dfrac{48}{4}}\\\\\mathsf{= 48\div4}\\\\\mathsf{\boxed{\bf = 12}}[/tex]

[tex]\boxed{\mathsf{x > 12}}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \bf NO, because }\mathsf{\bf x < 12}\large\text{ \bf \& it is an O.P.E.N. circle shaded}}}\\\boxed{\boxed{\large\text{\bf the right}}}\huge\checkmark[/tex]

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

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

Answer:

5 2/3

Step-by-step explanation:

:)

it would be A. 5 and 2/3

brainliest..

Answer:

75°

Step-by-step explanation:

The chord- chord angle is half the sum of of the arcs intercepted by the angle and its vertical angle, then

∠ 1 = [tex]\frac{1}{2}[/tex] (110 + 40)° = 0.5 × 150° = 75°

Answer:

Tim read 81 pages.

Step-by-step explanation:

If he read 3 pages on Monday and tripled the amount of pages he red based of off the amount of pages he read the previous day, he would have read 3 pages on Monday, 9 pages on Tuesday, 27 pages on Wednesday, and 81 pages on Thursday.

Monday: 3

Tuesday: 3 x 3 = 9

Wednesday: 9 x 3 = 27

Thursday: 27 x 3 = 81

I hope this helps you! :D

Answer:

1.465 years

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 per year,

Then, to solve for time t, when compound interest is compounded continuously, the formula is given as:

t = ln(A/P) / r

Where

A = Amount after time t = $5,789.00

P = Principal = Initial amount = $5,00

r = 0.1

Hence,

t = ln(5,789.00/5,000.00) / 0.1

t = 1.465 years

Therefore, the money was in the account for 1.465 years

Answer:

ur mom

Step-by-step explanation:

there is none, it's just simply ur mom

- hope that solved ur problem :)

- Im ur dad btw

- Mac and cheese is pretty good 10/10

- DADDY

Answer:

10x2 - 5 (the 2 has to be small too.)

Answer:

E)  x^5

Step-by-step explanation:

example, [tex]\sqrt{3}[/tex] = 3^1/2 where '1' is the coefficient of 3

[tex]\sqrt{3}[/tex] is the same as [tex]\sqrt[2]{3}[/tex] (it's assumed to be 2 unless another number is there)

so, √x^10 is the same as x^(10/2) which is x^5

Answer:

A.

Step-by-step explanation:

i pretty sure

Answer:

Yes, Chris will score

Step-by-step explanation:

Given the function :

F(x) = - 0.05(x - 16)² + 11

Distance from goal = 25

Height of goal = 8

Scoring condition, if ball isn't blocked :

If the ball travels a distance of 25 feets towards goal and elevation of ball isn't greater than 8 feets, then Chris will score ;

Function which models ball height with respect to distance, x

Put x = 25 in the equation and se if f(x) < 8 feets

F(25) = - 0.05(25 - 16)² + 11

F(25) = - 0.05(9)² + 11

F(25) = - 0.05 * 81 + 11

F(25) = - 4.05 + 11

F(25) = 6.95 feets

Hence, Chris would score if ball isn't vlaocjed by DeShawn because the height of ball is lower than the height of the goal.

Answer:

one solution (-10, -2)

Step-by-step explanation:

i used desmos :)

Answer:

x = -11 5/17

Step-by-step explanation:

3x + 2y = 12

2x - 3y = -57

5x + y =  -45

y = -5x - 45

2x - 3 (-5x - 45) = -57

2x + 15x + 135 = -57

17x + 135 = -57

17x = -192

x = -11 5/17

Answer:

x≤21/10

Step-by-step explanation:

[tex] \frac{1}{5} - 2x \geqslant - 4 \\ - 2x \geqslant - 4 - \frac{1}{5 } \\ 2x \leqslant 4 + \frac{1}{5} \\ 2x \leqslant \frac{21}{5} \\ x \leqslant \frac{21}{10} [/tex]

Answer:

B-10⁰

Step-by-step explanation:

5 x 10 is 50, 4 x 10 is 40, add those and you get 90⁰

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle y = \sqrt{x - 3}[/tex]

[tex]\displaystyle y' = \frac{1}{2}[/tex]

Step 2: Differentiate

Step 3: Solve

Find coordinates

x-coordinate

y-coordinate

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e