Question 17 (5 points)
Determine the value of x in the isosceles trapezoid.
2x
х
x = 60°
x= 65°
x= 180°
*= 90°

Answer:

35.5

Step-by-step explanation:

1 5/2 + (8*4)= 35.5

(8*4)= 32

32+1 5/2

1 5/2=3 1/2

32+3 1/3

35.5 or 35 1/2

Answer:

8 and 10

Step-by-step explanation:

Given

[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{x+2}[/tex] = [tex]\frac{9}{40}[/tex] ← combine the fractions on the left side

[tex]\frac{x+2+x}{x(x+2)}[/tex] = [tex]\frac{9}{40}[/tex]

[tex]\frac{2x+2}{x^2+2x}[/tex] = [tex]\frac{9}{40}[/tex] ( cross- multiply )

9(x² + 2x) = 40(2x + 2) ← distribute both sides

9x² + 18x = 80x + 80 ( subtract 80x + 80 from both sides )

9x² - 62x - 80 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 9 × - 80 = - 720 and sum = - 62

The factors are - 72 and + 10

Use these factors to split the x- term

9x² - 72x + 10x - 80 = 0 ( factor the first/second and third/fourth terms )

9x(x - 8) + 10(x - 8) = 0 ← factor out (x - 8) from each term

(x - 8)(9x + 10) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

9x + 10 = 0 ⇒ 9x = - 10 ⇒ x = - [tex]\frac{10}{9}[/tex]

x is an integer , then x = 8 and x + 2 = 8 + 2 = 10

The integers are 8 and 10

Answers: Integers are x=8, x=10.

Answer:

10 has 2 digits

1000 has 4 digits

Difference of 2 digits

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { f(-9)= 0.48}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]f(x) = \frac{2x + 3}{4x + 5} \\[/tex]

For [tex]f(-9)[/tex], put "[tex]-9[/tex]" for every value of "[tex]x[/tex]".

[tex]↬f( - 9) = \frac{2( - 9) + 3}{4( - 9) + 5}\\ [/tex]

[tex]↬ f(-9) = \frac{ - 18 + 3}{ - 36 + 5} \\[/tex]

[tex]↬ f(-9) = \frac{ - 15}{ - 31}\\ [/tex]

[tex]↬ f(-9)= \frac{15}{31}\\ [/tex]

[tex] ↬f(-9)= 0.48\\ [/tex]

[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]

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

[tex]\mathsf{f(x) = \dfrac{2x + 3}{4x + 5}}[/tex]

[tex]\mathsf{y = \dfrac{ 2x + 3}{4x + 5}}[/tex]

[tex]\mathsf{y = \dfrac{2(-9) + 3}{4(-9) + 5}}[/tex]

[tex]\mathsf{2(-9)}[/tex]

[tex]\mathsf{\bf = -18}[/tex]

[tex]\mathsf{y = \dfrac{-18 + 3} {4(-9) + 5}}[/tex]

[tex]\mathsf{-18 + 3}\\\mathsf{= \bf -15}[/tex]

[tex]\mathsf{y = \dfrac{ -15} {4(-9) + 5}}[/tex]

[tex]\mathsf{4(-9)}\\\mathsf{\bf = -36}[/tex]

[tex]\mathsf{y = \dfrac{-15}{-36 + 5}}[/tex]

[tex]\mathsf{-36 + 5}\\\mathsf{= \bf-31}[/tex]

[tex]\mathsf{y = \dfrac{-15}{ -31}\rightarrow\boxed{\bf \dfrac{15}{31}}}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: } \boxed{\bf f(-9) = \dfrac{15}{31}}}}\huge\checkmark[/tex]

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

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

Answer:

[tex]40\ cm^3[/tex]

Step-by-step explanation:

Let the actual volume is V.

The measured volume of an object is 46 cubic cm  which was 15% high from the actual volume.

According to the given condition,

[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]

So, the actual volume was [tex]40\ cm^3[/tex].

Answer:

y-y1=m(x-x1)

y-4=3/4(x+4)

y=3/4x+7

Answer:

Reflected over y-axis

Answer:

Step-by-step explanation:

The first line has slope of a/b and the second one has slope of m/n.

As an ≠ bm ⇒ a.b ≠ m/n, the slopes are different.

Since the slopes are different the lines are not parallel, hence they intersect at one point.

This means there is one solution only.

ax + by = c and mx + ny = d and an # bm then these simultaneous equations have Only one common solution.

[tex]\sf{ }[/tex] [tex]\sf{ }[/tex]

Answer:5.7 D

Step-by-step explanation:

Answer:

sum of five and 3 is divided by n

Answer:

[tex]A=157.07\ cm^2[/tex]

Step-by-step explanation:

Given that,

The radius of a cylinder, r = 5 cm

Height of the cylinder, h = 5 cm

We need to find the lateral surface area of the  cylinder. The formula for the lateral surface area of the cylinder is given by :

[tex]A=2\pi r h[/tex]

Put all the values,

[tex]A=2\pi\times 5\times 5\\\\=157.07\ cm^2[/tex]

So, the lateral surface area of the cylinder is [tex]157.07\ cm^2[/tex].

Answer:

B) 67°C.

Step-by-step explanation:

Newton's Law of Cooling is given by:

[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]

Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.

We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.

And we want to find the temperature of the coffee after four minutes.

First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:

[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]

Take the integral of both sides:

[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]

Integrate:

[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]

Raise both sides to e:

[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]

The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:

[tex]\displaystyle T=Ce^{kt}+A[/tex]

We are given that A = 25. Hence:

[tex]\displaystyle T=Ce^{kt}+25[/tex]

Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:

[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]

Hence:

[tex]T=75e^{kt}+25[/tex]

We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.

So, T = 90 given that t = 1. Substitute:

[tex]90=75e^{k(1)}+25[/tex]

Solve for k:

[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]

Therefore:

[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]

Then after four minutes, the temperature of the coffee will be:

[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]

Hence, our answer is B.

Step-by-step explanation:

the systems of equations shown are parallel because they have the same slope

Answer:

Answer is A

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

Add all the numbers given =256 then take the mean and multiply it with 7 =334 then take 334_256=78 and done

Answer:

A.

by-step explanation:

m to k

1 to 1.609

Answer:

358

Step-by-step explanation:

the step by step is in the photo so look at it

Answer:

She can buy from 0 to 20 bags, but no more.

Answer:

b <3

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm going to take a giant leap here and guess that you are looking for how old this mammal hide is. At least that's what I'm going to work out for you. Filling in the formula is relatively easy as long as we remember that the initial amount of hide was 100%:

[tex]37=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get

[tex].37=e^{-.0001t}[/tex] In order to get that t down from its current position, we have to take the natural log of both sides. The reason we do natural log as opposed to common log is because the natural log will cancel out the e:

[tex]ln(.37)=ln(e^{-.0001t})[/tex] and again, because the log cancels out the e we have:

ln(.37) = -.0001t and divide both sides by -.0001 to get

t = 9942.5 years

Answer:

answer is 9943

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Fip numbers and change both signs when reflecting over y=-x

Answer:

C

Step-by-step explanation:

Answer:

B. -0.07

Step-by-step explanation:

Apply the Law of signs find θ.

Cos θ = (a² + b² - c²)/2ab

Where,

a = 7

b = 8

c = 11

Plug in the values

Cos θ = (7² + 8² - 11²)/2*7*8

Cos θ = (49 + 64 - 121)/112

Cos θ = -8/112

Cos θ = -0.0714285714

Cos θ = -0.07 (to 2 decimal places)

Answer:

Step-by-step explanation:

Given identity is,

[tex]\text{tanA}=\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}[/tex]

To prove this identity, we will take left side of the identity,

[tex]\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}=\pm\sqrt{\frac{1-(1-2\text{sin}^2A)}{1+(2\text{cos}^2A-1)} }[/tex]

                  [tex]=\pm\sqrt{\frac{1-1+2\text{sin}^2A}{1+2\text{cos}^2A-1} }[/tex]

                  [tex]=\pm\sqrt{\frac{2\text{sin}^2A}{2\text{cos}^2A} }[/tex]

                  [tex]=\pm(\sqrt{\text{tan}^2A})[/tex]

                  [tex]=\text{tanA}[/tex] [Right side of the identity]

Hence, proved.

Answer:

4x^4+3x^2y^2+9y^2

(2x^2)^2 + 2×2x^2×3y^2 + (3y^2)^2 - 9

(2x^2 + 3y^2)^2 - (3)^2

(2x^2 +3y^2+3)(2x^2+3y^3-3)

Answer:

y = 5x + 19

Step-by-step explanation:

y = 5x + b

4 = 5(-3) + b

4 = -15 + b

19 = b

Answer: [tex]\frac{5}{9}\ m[/tex]

Step-by-step explanation:

Given

Area of the rectangular piece of paper is [tex]A=\frac{1}{3}\ m^2[/tex]

Length of the paper is [tex]l=\frac{3}{5}\ m[/tex]

Suppose width of the paper is [tex]w[/tex]

Area is the multiplication of length and width

[tex]\therefore A=lw\\\\\Rightarrow \dfrac{1}{3}=\dfrac{3}{5}\times w\\\\\Rightarrow w=\dfrac{5}{9}\ m[/tex]

Thus, the width of the paper is [tex]\frac{5}{9}\ m[/tex]

Answer:

They are consecutive terms in the Fibonacci Sequence.

Step-by-step explanation:

The sequence goes 1,1,2,3,5,8,13,21,...

Since 13 and 21 are consecutive here, that is the answer.