what is the length of the diagonal of the rectangle?

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

In triangle TPQ,

As it is given that, RS || PQ

So, it means

⇛∠TRS = ∠TPQ [ Corresponding angles ]

⇛ ∠TSR = ∠TPQ [ Corresponding angles ]

[tex]\rm\implies \: \triangle TPQ \: \sim \: \triangle TRS \: \: \: \: \: \: \{AA \}[/tex]

Now, We know

Area Ratio Theorem,

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{ar( \triangle \: TRS)} = \dfrac{ {PQ}^{2} }{ {RS}^{2} } [/tex]

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = \dfrac{ {6}^{2} }{ {3}^{2} } [/tex]

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = \dfrac{36 }{9} [/tex]

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = 4 [/tex]

[tex]\rm\implies \:ar( \triangle \: TPQ) = 60 \: {cm}^{2} [/tex]

Answer:

a and f

Step-by-step explanation:

1500 is double 750, which is the combined calories of lunch and breakfast, which is only 1 third.

Answer:

1st and 2nd options

Step-by-step explanation:

Daily total = (400+350)*3 = 2250

Dinner = 2250 * 2/3 = 1500

equation: 2/3*(x+400+350) = 2/3 * daily total = Dinner = x

Answer:

18 crayon in both boxes.

Step-by-step explanation:

Asked:  Greatest number of equal crayons in both boxes.

Facts:

Number of crayons in pack 1 = 24

Number of crayons in pack 2 = 12

Total crayons in both packs  = 24 + 12 = 36

Plan:

If both packs need to have equal crayons, then it should be dived by 2.

Solution:

36 ÷ 2 = 18

Answer:  c

Step-by-step explanation:

and then when you add all of the given measurements you will have the distance from clear lake to the end of her hike

Answer:

475767u5yttuyy

Step-by-step explanation:

phobrovicodibfofiffivonf

I think it's 0.075 inch per year

Answer:

Your answer is C. or 0.075 inches per year.

Step-by-step explanation:

251-248 = 3 ( To figure out how much it grew )

2005 -1965 = 40   ( To figure out how long it took )

3/40 = 0.075

Answer:

52

Step-by-step explanation:

62-10

Answer:

What fair

Step-by-step explanation:

Step-by-step explanation:

answer/ explanation is in the picture

Answer:

2.02units

Step-by-step explanation:

tan68°=[tex]\frac{5}{x}[/tex]=2.4750868534163,so x ≈2

Answer:

My answer is -9.becasiug

Step-by-step explanation:

there seems to be something missing.

I assume the slope of the line is -2/3.

the slope of a line is always the factor of x in the equation.

the slope is the y/x ratio indicating how many units y changes, when x changes by a certain amount of units (e.g. when going from one point on the line to another).

the equation for the line looks like this then :

y = (-2/3)×x + b

to get b we use the provided point (-6, -5) and it's x and y values.

-5 = (-2/3)×-6 + b = 4 + b

b = -9

so, the full equation of the line is

y = (-2/3)×x - 9

Answer: To Get both numeric terms on the right side, for example add 16 to both sides of the equation

Happy To help ;)

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

∠ C ≈ 22.6°

Step-by-step explanation:

Since Δ ABC is right at B

Using the sine ratio in the right triangle

sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{5}{13}[/tex] , then

∠ C = [tex]sin^{-1}[/tex] ( [tex]\frac{5}{13}[/tex] ) ≈ 22.6° ( to 1 dec. place )

Answer:

[tex]\sf\longmapsto\sf\boxed {x = 1}[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: 2x + 10 = 12[/tex]

[tex]\sf\longmapsto \: \: 2x + 10 - 10 = 12 - 10[/tex]

[tex]\sf\longmapsto \: 2x = 2[/tex]

[tex]\sf\longmapsto \: \frac{2x}{2} = \frac{2}{2} [/tex]

[tex]\sf\longmapsto \: x = 1[/tex]

Answer:

[tex]\boxed {\sf x=1}[/tex]

Step-by-step explanation:

[tex]\sf 2x+10=12[/tex]

[tex]\boxed{\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}}[/tex]

[tex]\boxed{\mathrm{Divide\:both\:sides\:by\:}2}[/tex]

[tex]\boxed{\sf Hope\: it\:helps!}[/tex]

Answer:

10 because 19 - 9 = 10 it works the same way for addition just swap the signs

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The number of terms in the given expression is 3, so it is a Trinomial

5x^2 + 3x - 3 is a trinomial.

A monomial is an expression that has one term, such as 3x.

A binomial is an expression that has two terms, such as 4x^2 + 6x or 4x - 6.

A trinomial is an expression that has three terms, such as x^2 + 5x + 6.

Hope this helps!! :)

Answer:

false

Step-by-step explanation:

Step-by-step explanation:

wjjdjrjdjdjdudidjdkdk pick the C

Answer:

D,

Step-by-step explanation:

Step 1: 47-12=27, 27+(-27)=0

step 2: 27/2=13.5, 2c/2=c

step 3, change 13.5 to fraction which is 13 1/2

(hope it's helpful :)

Given :-

To find :-

Solution :-

General Equation of slope intercept form ,

Here c = 0 , so its y intercept will be (0,0) . Hence it will pass through origin .

Answer:

1. B 1/3

2. C 12

1) 1/3

2) 12

ur welcome:)

Answer:

You have the correct answer selected, (C.) Die stock. I hope this helps you! Good luck! : )

Answer:

10.50

Step-by-step explanation:

in total she would have spent 10.50 because 8.75 for the peaches and 1.75 for the ice cream sandwich

Answer:

For the red triangle the width is 9 cm and the length is 24 cm. For the blue triangle, the width is 14 cm and the length is 22 cm.

Step-by-step explanation:

Red triangle: width is 9 cm, length is 24 cm, blue one width is 14 cm and the length is 22 cm. hope this helps. did this quickly! <3

Answer:

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the width of the red rectangle

Step 3. Let w+15 be the length of the red rectangle

Step 4. Let w+5 be the width of the blue rectangle

Step 5. Let w+15-2=w+13 be the length of the blue rectangle

Step 6. Then for the blue rectangle, P=w+5+w+5+w+13+w+13=4w+36=72

Step 7. Solving 4w+36=72  

Subtract 36 from both sides of the equation

4w=36

Divide by 4 to both sides of the equation

ANSWER: For the red triangle the width is 9 cm and the length is 24 cm. For the blue triangle, the width is 14 cm and the length is 22 cm.

Answer:

1st option

y=-3/8x+3

Translating the situation to a mathematical sentence, and solving, we find that the solutions are: [tex]x = 5 \pm 3\sqrt{2}[/tex]

The translation of the problem given is:

[tex](x - 5)^2 + 1 = 19[/tex]

Then, solving:

[tex](x - 5)^2 = 18[/tex]

[tex]x^2 - 10x + 25 = 18[/tex]

[tex]x^2 - 10x + 7 = 0[/tex]

Which is a quadratic equation with [tex]a = 1, b = -10, c = 7[/tex]. Then:

[tex]\Delta = (-10)^{2} - 4(1)(7) = 72[/tex]

[tex]x_{1} = \frac{-(10) + \sqrt{72}}{2}[/tex]

[tex]x_{2} = \frac{-(-10) - \sqrt{72}}{2}[/tex]  

[tex]\sqrt{72} = \sqrt{9 \times 8} = \sqrt{3^2 \times 2^3} = 6\sqrt{2}[/tex], then:

[tex]x_1 = 5 + 3\sqrt{2}[/tex]

[tex]x_2 = 5 - 3\sqrt{2}[/tex]

The solutions are [tex]x = 5 \pm 3\sqrt{2}[/tex]

A similar problem is given at https://brainly.com/question/13094243

Answer:

$11.90

Step-by-step explanation:

79.30 times 0.15

Answer:

The answer is 11.895. That's the exact answer.

Step-by-step explanation:

Original price X Discount %

The three equivalent ratios are 6/1 gallons/minute, 1/40 quarts/second and 360/1 gallons/hour.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, Tiffany can fill the pool at a rate of 1/10 gallons per second.

Equivalent ratios are the ratios that are the same when we compare them.

We know that, 60 seconds =1 minute

1/10 × 60 = 6 gallons/minute

1 gallon = 4 quarts

1/10 = 1/10×4 = 1/40 quarts/second

1 hour =60 minute

So, 6 gallons/minute =6×60

= 360 gallons/hour

Here, 6 gallons/minute = 1/40 quarts/second = 360 gallons/hour

Therefore, the three equivalent ratios are 6/1 gallons/minute, 1/40 quarts/second and 360/1 gallons/hour.

To learn more about the ratio visit:

brainly.com/question/13419413.

#SPJ2

Answer:

The answer to this question is 8×10−8. I hope this helps you! :D

Answer:

8*10^-8

[tex]ie.8 \times {10}^{ - 8} [/tex]