in a triangle the angle with the smallest measure is always the opposite the​

Answer:

G

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplifying the radicals in the expression

[tex]\sqrt{52}[/tex]

= [tex]\sqrt{4(13)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{13}[/tex]

= 2[tex]\sqrt{13}[/tex]

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

[tex]\sqrt{117}[/tex]

= [tex]\sqrt{9(13)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]

= 3[tex]\sqrt{13}[/tex]

Then

[tex]\sqrt{52}[/tex] + [tex]\sqrt{117}[/tex]

= 2[tex]\sqrt{13}[/tex] + 3[tex]\sqrt{13}[/tex]

= 5[tex]\sqrt{13}[/tex] → G

[tex]{\small\sf{The\:expression \sqrt{52} + \sqrt{117} \:is \: equivalent \: to}}[/tex]

[tex]\small\bf{F.} \: \sf{13} [/tex]

[tex]\small\bf{G.}\sf \:5 \sqrt{13} [/tex]

[tex]\small\bf{H.}\sf\:6 \sqrt{13} [/tex]

[tex]\small\bf{J.}\sf\:13 \sqrt{13} [/tex]

[tex]\small\sqrt{52}+\sqrt{117}\sqrt{4•13} +\sqrt{9•13}\tiny\sf\purple{(Product\:Property)}[/tex]

[tex]\small{ \: \:\: \: \: \: \: \:=\sqrt{2²•13}+\sqrt{3²•13}\tiny\sf\purple{(Prime\:Factorization)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=\sqrt{2²}\sqrt{13}+\sqrt{3²}\sqrt{13}\tiny\sf\purple{(Product\:Property)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=2\sqrt{13}+3\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=5\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]

So, the correct option is D.

#Hope it helps!

(ノ^_^)ノ

1

is the correct answer lol ez stuff

==============================================

Explanation:

The recursive rule

f(n+1)=f(n)-3

can be rearranged to

f(n) = f(n+1)+3

after adding 3 to both sides

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

Now let's say we plug in n = 3

f(n) = f(n+1)+3

f(3) = f(3+1)+3

f(3) = f(4)+3

f(3) = 22+3

f(3) = 25

Repeat for n = 2

f(n) = f(n+1)+3

f(2) = f(2+1)+3

f(2) = f(3)+3

f(2) = 25+3

f(2) = 28

Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).

Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.

Answer:

-14

Explanation:

Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.

Formula for calculating price elasticity is: change in price/change in quantity =dq/dp

Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:

2p+2+dq/dp=0

dq/dp=-2p-2

Given p =6, we substitute:

dq/dp=-2×6-2

dq/dp=-12-2

dq/dp=-14

With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.

Answer:

y = 0.9

Step-by-step explanation:

1.05 + 0.7y = 3.5y - 1.47

-3.5y + 0.7y = -1.47 - 1.05

-2.8y = -2.52

y = 9/10 = 0.9

Answer:

[tex]\textbf{HELLO!!}[/tex]

[tex]0.7\left(1.5+y\right)=3.5y-1.47[/tex]

[tex]1.05+0.7y=3.5y-1.47 \gets \textsl{Expand}[/tex]

[tex]1.05+0.7y-1.05=3.5y-1.47-1.05 \gets Subtract\; 1.05 \from\:both\:sides[/tex]

[tex]0.7y=3.5y-2.52[/tex]

[tex]0.7y-3.5y=3.5y-2.52-3.5y[/tex]

[tex]\mathrm{Subtract\:}3.5y\mathrm{\:from\:both\:sides} \nwarrow[/tex]

[tex]-2.8y=-2.52[/tex]

[tex]\frac{-2.8y}{-2.8}=\frac{-2.52}{-2.8} \hookleftarrow \mathrm{Divide\:both\:sides\:by\:}-2.8[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{y=0.9}}}}}[/tex]

[tex]\bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet[/tex]

[tex]\textbf{HOPE IT HELPS}[/tex]

[tex]\textbf{HAVE A GREAT DAY!!}[/tex]

Answer:

[tex]\textbf{HELLO!!}[/tex]

[tex]2p=2[/tex]

[tex]\frac{2p}{2}=\frac{2}{2}[/tex] [tex]\hookleftarrow \mathrm{Divide\:both\:sides\:by\:}2[/tex]

[tex]=1[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{P=1}}}}}[/tex]

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

[tex]q - 3 = 7[/tex]

[tex]q-3+3=7+3[/tex] [tex]\hookleftarrow \mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex]

[tex]=10[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{q=10}}}}}[/tex]

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

[tex]\textbf{HOPE IT HELPS}[/tex]

[tex]\textbf{HAVE A GREAT DAY!!}[/tex]

Answer:

The slope of the line is [tex]-\frac{1}{5}[/tex]  in fraction form or -0.2 in decimal form.

Step-by-step explanation:

To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

For finding the slope of this line with the points (-2,-1) and (8,-3), start by writing down the information given from the question.

[tex]y_{2}= -3[/tex]

[tex]y_{1}=-1[/tex]

[tex]x_{2}=8[/tex]

[tex]x_{1}= -2[/tex]

Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(-1)}{8-(-2)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-2}{10}= -\frac{1}{5}[/tex]. The final answer will be [tex]-\frac{1}{5}[/tex]  in fraction form or -0.2 in decimal form.

Answer:

[tex]\cos(2\, x) = 1 - 2\, (\sin(x))^2[/tex].

Step-by-step explanation:

Angle sum identity for cosine: [tex]\cos(a + b) = \cos(a) \, \cos(b) - \sin(a) \, \sin(b)[/tex].

Pythagorean identity: [tex](\cos(a))^{2} + (\sin(a))^{2} = 1[/tex] for all real [tex]a[/tex].

Subtract [tex](\cos(x))^{2}[/tex] from both sides of the Pythagorean identity to obtain: [tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex].

Apply angle sum identity to rewrite [tex]\cos(2\, x)[/tex].

[tex]\begin{aligned}&\cos(2\, x)\\ &= \cos(x + x) \\ &= \cos(x) \, \cos(x) - \sin(x)\, \sin(x) \\ &= (\cos(x))^{2} + (\sin(x))^{2}\end{aligned}[/tex].

[tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex] follows from the Pythagorean identity. Hence, it would be possible to replace the [tex](\cos(x))^{2}[/tex] in the previous expression with [tex](1 - (\sin(x))^{2})[/tex].

[tex]\begin{aligned}&(\cos(x))^{2} - (\sin(x))^{2}\\ &= \left[1 - (\sin(x))^{2}\right] - (\sin(x))^{2} \\ &= 1 - 2\, (\sin(x))^{2} \end{aligned}[/tex].

Conclusion:

[tex]\begin{aligned}&\cos(2\, x) \\ &= (\cos(x))^{2} + (\sin(x))^{2} \\ &=1 - 2\, (\sin(x))^{2}\end{aligned}[/tex]

Answer:

a. 8 cm

Step-by-step explanation:

Given:

EH = 6 cm

FG = 4.00 cm

Based on the mid-segment theorem of a trapezoid, we have:

EH = ½(FG + DI)

Plug in the values

6 = ½(4 + DI)

Multiply both sides by 2

6*2 = 4 + DI

12 = 4 + DI

12 - 4 = 4 + DI - 4

8 = DI

DI = 8 cm

The solution is given below.

A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

here, we have,

Refer to the fraction strip to show 3/4 & 6/8 are same.

Also if you reduce 6/8 by dividing 2 to numerator & denominator…

it’s 3/4.

The solution is attached below.

To learn more on number line click:

brainly.com/question/29162579

#SPJ2

Answer:

She will be 17

Step-by-step explanation:

My sister is like that but she's graduating in 22'

It sort of depends where Sarah lives -.-  

But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.

So 15 plus 3.

Sarah will be 18 when she graduates high school.

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: {b}^{2} + 2b - 24}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

[tex] \: (b + 6)(b - 4)[/tex]

➼[tex] \: b \: (b - 4) + 6 \: (b - 4)[/tex]

➼[tex] \: {b}^{2} - 4b + 6b - 24[/tex]

Combining like terms, we have

➼[tex] \: {b}^{2} + 2b - 24[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

9514 1404 393

Answer:

  20%

Step-by-step explanation:

100 mL of the drink is coffee

The total amount of drink is 100 mL +400 mL = 500 mL. Then the fraction that is coffee is ...

  coffee/total = (100 mL)/(500 mL) = 1/5 = 1/5 × 100% = 20%

20% of Donna's drink is coffee.

Answer:

20%

Step-by-step explanation:

6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.

Answer:

Step-by-step explanation:

hope it's helpful :-)

Answer:

(a) The time to complete 1 cycle and return is 16/3

(b) The minimum height is 30 inches and the maximum is 54 inches

Step-by-step explanation:

Given

[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]

Solving (a): Time to complete 1 cycle and return

This implies that we calculate the period.  This is calculated using:

[tex]T = \frac{2\pi}{w}[/tex]

Where:

[tex]w =\frac{3\pi}{8}[/tex]

So, we have:

[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]

[tex]T = \frac{2}{\frac{3}{8}}[/tex]

[tex]T = \frac{2*8}{3}[/tex]

[tex]T = \frac{16}{3}[/tex]

Solving (b): The maximum and the minimum height

To do this, we have:

[tex]-1 \le \sin(\theta) \le 1[/tex]

Which means:

[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]

So, the minimum is:

[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]

And the maximum is:

[tex]\sin(\frac{3\pi}{8}) =1[/tex]

Recall that the height is:

[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]

So, the maximum and the minimum of  are:

[tex]h_{min} =12 * -1 + 42[/tex]

[tex]h_{min} =30[/tex]

and

[tex]h_{max} =12*1+42[/tex]

[tex]h_{max} =54[/tex]

Answer:

D. ✔ 28

Step-by-step explanation:

E 2021

Answer:

The Probability would be 2.78%

Step-by-step explanation: Hope this helps :)

Answer:

(a) $83 for 6 snacks

(b) [tex]y = 65 + 3x[/tex] --- for x snacks

Step-by-step explanation:

Given

Let:

[tex]n \to people[/tex]

[tex]ticket =\$13[/tex] --- per individual

[tex]snacks = \$3[/tex] --- per individual

Solving (a): Amount for 6 snacks

The amount paid (y) is:

[tex]y = ticket * n + snacks * 6[/tex] ---- because she bought 6 snacks

[tex]y = 13 * n + 3 * 6[/tex]

[tex]y = 13n + 18[/tex]

[tex]n = 5[/tex] ---- Annabelle and the 4 kids.

So:

[tex]y =13*5+18[/tex]

[tex]y =65+18[/tex]

[tex]y =83[/tex]

Solving (b): For x snacks

The amount paid (y) is:

[tex]y = ticket * n + snacks * x[/tex] ---- because she bought x snacks

[tex]y = 13* 5 + 3* x[/tex]

[tex]y = 65 + 3x[/tex]

Answer:

Step-by-step explanation:

for circle

diameter = 26 cm

radius = diamtere/2

=26/2

=13 cm

area of circle  = πr^2

=3.14^13^2

=3.14*169

=530.66 cm^2

=531 cm^2   (after round off )

area of square= l^2

=5.1^2

=26.01 mi^2

are of rectangle = l *b

=6*5.1

=30.6 m^2

area of triangle = base*height / 2

=9*6.4 / 2

=57.6 / 2

=28.8 yd^2

Answer:

r = 5 units

Step-by-step explanation:

Given:

Angle subtended at the centre (∅) in radians = 2π/3

Arc length (S) = 10π/3

radius (r) = ?

Required:

Radius (r)

Solution:

Formula for arc length given the central angle in radians is:

S = r∅

Make e the subject of the formula by dividing both sides by ∅

S/∅ = r∅/∅

r = S/∅

Plug in the values

r = (10π/3) / (2π/3)

Change the operation sign to multiplication and turn the fraction by your right upside down

r = 10π/3 × 3/2π

r = (10π × 3)/(3 × 2π)

Cross out terms that can divided each other

r = 5

Answer:

12

Step-by-step explanation:

Since there is no diagram. I will just tell you the answer. first convert into multiplcation keep everything but the 1/3. Change 1/3 into 3/1 (3). Multiply 4*3=12.

Sorry if I don't have a graph.

Hope this helps!

Answer:

12/1=60/5

1/12=60/5

Answer:

B and C

Step-by-step explanation:

Answer:

tom sleep 14hour my ans lt might help you

Answer:

D. The coefficient of determination is the ratio of the explained variation to the total variation.

C. The coefficient of determination is the percent of variation of y that is explained by the relationship between x and y

Step-by-step explanation:

The Coefficient of determination is the ratio of the explained variation in y to the total variation in y.

Coefficient of determination, r² ;

r² = explained variation / total variation

The coefficient of determination is the proportion of variation in y (predicted value) which is due to the regression line ; Hence, it is the percent of variation of y that is explained by the relationship between x and y.

Answer:

a. 0.403

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

Confidence interval of (0.253,0.553)

The bounds are 0.253 and 0.553, so the point estimate is:

[tex]p = \frac{0.253 + 0.553}{2} = 0.403[/tex]

This means that the correct answer is given by option A.

Answer:

(1/2)(2)(5+3)

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The area of a trapezoid is:

( a + b ) ÷ 2 x h

Where a & b are the bases, and h is the height.

Use formula with the given measurements:

(3 + 5) ÷ 2 x 2

= 8 ÷ 2 x 2

= 4 x 2

= 8

Hope this helps

Answer:

It is D.

Step-by-step explanation:

x ≤ 3 or x ≥ –1

Answer:

D) X <_ 3 or X _> -1

Whole Unit Test Review Answers:

1) D

2)D

3)B

4)C

5)D

6)A

7)B

8)C

9)A

10)B

11)D

12)D

13)B

14)B

15)D

(I got a 100%, and these were my answers, hope they help!)

(The pic below is a screenshot of the 100%, for reassurance)

Answer:

x2+y2−12x+4y−60=0

The center of the circle is point: C=(6,−2).

The radius of the circle is r=10.