7a - 2b = 5a + b

a = 2b
a = 3b
a = a equals StartFraction 3 Over 2 EndFraction b.b
a = a equals StartFraction 2 Over 3 EndFraction b.b

Answer:

12/1=60/5

1/12=60/5

Answer:

B and C

Step-by-step explanation:

Answer:

Step-by-step explanation:x=2y-8

4y=3.(2y-8)+6

4y=6y-24+6

4y-6y=-24+6

-2y=-18

Y=9

X=2Y-8

x=2.9-8=10

Answer:

in a triangle, the angle with the smallest measure is always opposite the shortest side.

Step-by-step explanation:

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]

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:

[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]

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the weights of the large and small boxes, respectively. The problem statement gives rise to the system of equations ...

  x + y = 85 . . . . . combined weight of a large and small box

  70x +50y = 5350 . . . . combined weight of 70 large and 50 small boxes

We can subtract 50 times the first equation from the second to find the weight of a large box.

  (70x +50y) -50(x +y) = (5350) -50(85)

  20x = 1100 . . . . simplify

  x = 55 . . . . . . . divide by 20

Using this in the first equation, we can find the weight of a small box.

  55 +y = 85

  y = 30 . . . . . . . subtract 55

A large box weighs 55 pounds; a small box weighs 30 pounds.

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:

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:

A i think

Step-by-step explanation:

edge 2021

The simplified expression is - f(x) = [tex]log_{2} (\frac{x^{3} (x+4)}{3}})[/tex]

We have the following statement -

3 log Subscript 2 Baseline x minus (log Subscript 2 Baseline 3 minus log Subscript 2 Baseline (x + 4))

We have to convert it into Single logarithm.

Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

[tex]log_{b} (b^{x} ) = x[/tex]

According to the question, We can write the given statement in the mathematical form as follows -

f(x) = [tex]3\;log_{2} (x )-[log_{2} (3) -log_{2} (x+4)][/tex]

Using the property of logarithm -

log (A) - log(B) = log ([tex]\frac{A}{B}[/tex]), we get -

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

Using the property of logarithm -

[tex]a\;log (b) = log(b^{a})[/tex]

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

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

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

Hence, the simplified expression is - f(x) = [tex]log_{2} (\frac{x^{3} (x+4)}{3}})[/tex]

To solve more questions on logarithms, visit the link below -

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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:

(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:

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.

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:

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Answer:

tom sleep 14hour my ans lt might help you

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:

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:

The Third one

Step-by-step explanation:

Your Welcome :)

Graph of the function is attached below.

Correct option is D.

As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:

Definition of exponential function

In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant  called the base of the function, which must be greater than 0.

Given, exponential function

f(x) = (1/4)4ˣ

exponential function is defined for x∈R

Putting x = 0

f(0) = (1/4)4⁰

f(0) = 1/4

Point on curve is (0,1/4)

Putting x = 1

f(1) = (1/4)4¹

f(1) = (1/4)4

f(1) = 1

Point on curve is (1,1)

Putting x = 2

f(2) = (1/4)4²

f(2) = (1/4)16

f(2) = 4

Point on curve is (2,4)

Putting x = 3

f(3) = (1/4)4³

f(3) = (1/4)64

f(3) = 16

Point on curve is (3,16)

Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.

Hence, graph of the function is drawn as follows.

Learn more about exponential function here:

https://brainly.com/question/14355665

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Answer:

|-2| + |5|

Step-by-step explanation:

Dennis walks from (–5, –2) to (–5, 5) on the map.

Point on the format (x,y). On the x-coordinate, he stayed at the same position, x = -5, so it does not enter the distance calculation.

On the y-coordinate, he went from -2 to 5, so the distance is of:

[tex]d = 5 - (-2) = 5 + 2 = |5| + |2| = |5| + |-2| = 7[/tex]

So the correct option is |-2| + |5|

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.

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:

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:

(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:

D. ✔ 28

Step-by-step explanation:

E 2021

9514 1404 393

Answer:

Step-by-step explanation:

The lengths of the sides can be found using the distance formula.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  AC = √((0 -(-2))^2 +(8 -2)^2) = √(4+36) = 2√10

  BC = √((0 -6)^2 +(8 -2)^2) = √(36+36) = 6√2

The distance AB is the difference of the x-coordinates of the points: 6-(-2) = 8.

Then the perimeter is ...

  P = a + b + c = 6√2 +2√10 +8 = 8.49 +6.32 +8 = 22.81 . . . units

__

The height of the triangle is the difference in y-values between vertex C and line AB: 8 -2 = 6. The area is given by the formula ...

  A = 1/2bh

  A = 1/2(8)(6) = 24 . . . square units

[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]

Answer:

the perdom

Step-by-step explanation:

Answer:

3

Step-by-step explanation: