An ice sculpture is melting because of heat. Assuming its height changes bynegative 5 over 32m every hour, what will be the change in height after 4 hours? negative 20 over 8 meters 5 over 8 meter negative 5 over 32 meter negative 5 over 8 meter

Answer:

a = -27

Step-by-step explanation:

-2⁄3 a − 6 = 12

add 6 to both sides:-

-2/3 a -6 + 6 = 12 + 6

-2/3 a = 18

Now multiply each side by -3/2:-

a = 18 * -3/2 =  -54/2

=  -27

To solve the equation -2⁄3 a - 6 = 12 for 'a', add 6 to both sides of the equation and then multiply both sides of the equation by -3/2 to isolate the variable 'a'. The value of 'a' that satisfies the equation is a = -27.

To solve the equation -2⁄3 a - 6 = 12 for 'a', we can start by isolating the variable on one side of the equation. First, let's add 6 to both sides of the equation:

-2⁄3 a - 6 + 6 = 12 + 6

-2⁄3 a = 18

Next, we can multiply both sides of the equation by -3/2 to get:

(-3/2)(-2/3 a) = (-3/2)(18)

a = -27

The value of 'a' that satisfies the equation -2⁄3 a - 6 = 12 is a = -27.

Answer:

52 miles

Step-by-step explanation:

We can use a ratio to solve this problem.  Let put miles over time.  We know that 1 hour = 60 minutes.  We need to have the units the same.

130 miles          x miles

--------------     = ---------------

150 minutes      60 minutes

Using cross products

130 * 60 = 150 x

Divide each side by 150

130/150 * 60 = 150x/150

52 =x

Answer:

Point-Slope form: The equation of line is given by:

[tex]y-y_1=m(x-x_1)[/tex]              ......[1]

where m is the slope and [tex](x_1,y_1)[/tex] is the point on the line.

From the given graph:

Consider two points i.e,

[tex](0, 1)[/tex] and (-0.5, 0)

Calculate slope:

Formula for slope is given by;

[tex]\text{Slope}(m) = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given values we have;

[tex]m = \frac{0-1}{-0.5-0} = \frac{-1}{-0.5} = \frac{10}{5} =2[/tex]

Now, substitute the value of m = 2 and (0, 1) in equation [1] we have;

[tex]y-1 = 2(x-0)[/tex]

y-1 = 2x

Add 1 to both sides we get;

y = 2x+1

On comparing equation y = 2x+1 with the slope intercept form of a line (i.e, y = mx+b) then we have;

slope(m) = 2

y-intercept(b) = 1

therefore, the slope of the function:

m = 2

y-intercept(b) = 1

and the equation represents the graph: y = 2x+1

Answer:

2

1

y = 2x + 1

Step-by-step explanation:

[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{x^2+7x+6x+42}=\dfrac{7(x+6)}{x(x+7)+6(x+7)}\\\\=\dfrac{7(x+6)}{(x+7)(x+6)}=\boxed{\dfrac{7}{x+7}}[/tex]

Your answer should be 2(10x^3+21x^2+21) over X^2 2(10x^3+21x^2+21)/X^2 unless the / was a fraction symbol and not a division symbol then your answer would be 7 over x+7 7/x+7

Answer:

90

Step-by-step explanation:

The first term  = 6* 2^0 =  6

The second term = 6 * 2^ (2-1) = 6*2 = 12

The third term = 6* 2^(3-1) = 6*2^2 = 6*4 = 24

The fourth term = 6* 2^(4-1) = 6* 2^3 = 6*8 = 48

S4  is the sum of the 1st four terms

S4 = 6+ 12+24+ 48 = 90

The reference angle for [tex]31\pi[/tex] 6 by conversion of radians to degrees is [tex]210^o[/tex].

One radian is defined as the angle formed by the center of a circle intersecting an arc of length equal to the radius of the circle.

There are [tex]\pi[/tex] radians in [tex]180^o[/tex], So,[tex]\dfrac{31\pi}{6}[/tex] must be multiplied by [tex]\dfrac{180}{\pi}[/tex]to obtain the angle in degrees.

[tex]\dfrac{31\p}{6} \times \dfrac{180}{\pi}[/tex]

= [tex]\dfrac{31 \times 180}{6}[/tex]

=[tex]31 \times 30[/tex]

= [tex]930^o[/tex]

Since the reference angle is always positive and is formed with the x-axis, we need to find the acute angle formed between the terminal side of the angle and the positive x-axis.

The reference angle can be calculated by subtracting the closest multiple  [tex]180^o[/tex] from the angle in degrees.

[tex]930^o - 2\times 180^o[/tex]

= [tex]930^o - 360^o[/tex]

=[tex]570^o[/tex]

However, the reference angle should always be between [tex]0^o[/tex] and [tex]180^o[/tex] So, we take the smaller angle, which is

[tex]570^o- 360^o[/tex]

= [tex]210^o[/tex]

Therefore, the reference angle in degrees  [tex]31\pi6[/tex] is [tex]210^o[/tex]

Learn more about reference angles here:

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The reference angle of the given angle is [tex]30\textdegree.[/tex]

Converting the given angle from radians to degrees:

We know that [tex]\pi[/tex] radians is equal to 180°. Therefore,

[tex]\frac{31\pi}{6}\ radians \times \frac{180\textdegree}{\pi} = \frac{31}{6}\times 180 = 930\textdegree[/tex]

Finding the equivalent angle between 0° and 360°:

Since 930° is greater than 360°, an equivalent angle needs to be found by subtracting multiples of 360° until an angle between 0° and 360° is obtained.

930°−2×360°=930°−720°=210°

Determining the reference angle:

The reference angle is the acute angle that the given angle makes with the x-axis. Since 210° is in the third quadrant, calculating the reference angle as:

210°−180°=30°

Therefore, the reference angle for [tex]\frac{31\pi}{6}[/tex]​ is 30°.

24 = 2 · 2 · 2 · 3

36 = 2 · 2 · 3 · 3

GCF(24, 36) = 2 · 2 · 3 = 12

24 = 12 · 2

36 = 12 ·3

24 + 36 = 12 × 2 + 12 × 3 = 12 × (2 + 3)

The result of factoring out the Greatest Common Factor (GCF) from the expression (24 + 36) is 12 × (2 + 3).

To factor out the Greatest Common Factor (GCF) from the expression (24 + 36), we first need to determine the largest number that divides evenly into both 24 and 36. The GCF of 24 and 36 is 12. We divide each term by the GCF to factor out it from the expression:

24 ÷ 12 = 2

36 ÷ 12 = 3

Thus the expression factored out by the GCF is 12 × (2 + 3).

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Answer:

121/100

Hope it helps!

Answer:

The temperature yesterday was -6 because 7-13 is -6.

Step-by-step explanation:

Answer:

The yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.

Step-by-step explanation:

The temperature today is 7 degrees Celsius. Yesterday was 13 degrees Celsius cooler. That the temperature is colder means that the temperature was lower than today's temperature. This means that to obtain the temperature on the previous day, 13°C must be subtracted from today's temperature.

yesterday’s temperature=today’s temperature-13°C

It is now possible to replace today's temperature with 7 ° C

yesterday’s temperature=7°C-13°C

Remember that to subtract two integers of a different sign (one positive and the other negative), as in this case, you must subtract their absolute values (that is, subtract 13-7 = 6), and the answer will have the same sign as the number with the highest absolute value (absolute value or module of any real number is the same number but with a positive sign). As in absolute value 13 is greater than 7, the answer to the subtraction will be negative

yesterday’s temperature=7°C-13°C

So, finally, the yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.

Answer:

side X is 5 and side k is 6

Step-by-step explanation:

Answer:

Multiply 1/4 ; dividing 4

Step-by-step explanation:

Note that in each number going from left to right, it decreases by dividing 4 each time (or multiplying 1/4)

8/4 = 2 ; 2/4 = 1/2 ; (1/2)/(4) = 1/8 ; etc.

(8)(1/4) = 2 ; (2)(1/4) = 1/2 ; etc.

~

Answer: 1/4

Step-by-step explanation:

2x - y = 5      subtract 2x from both sides

2x - 2x - y = 5 - 2x

- y = 5 - 2x

The sign "-" (minus) before y was lost.

Final answer:

The room is not a square, as shown by applying the Pythagorean theorem, because the calculated diagonal of a square with 17-inch sides would be approximately 24.04 inches, not 18.79 inches.

Explanation:

To determine if the room is in the shape of a square, we can use the Pythagorean theorem, which relates the lengths of the sides of a right-angled triangle. For a square, the lengths of all four sides are equal. Therefore, if we assume that the length and the width of the room are both equal to the given wall length of 17 inches, the diagonal (d) of the square can be calculated using the Pythagorean theorem:

c2 = a2 + b2
where c is the length of the diagonal, and a and b are the lengths of the sides of the square.

So, it would be:

c2 = 172 + 172
    = 289 + 289
    = 578

Now we find the square root of 578 to find the length of the diagonal (c):

c ≈ √578 ≈ 24.04 inches

Since the given diagonal length is approximately 18.79 inches, and our calculated value for the diagonal of a square with sides 17 inches is approximately 24.04 inches, the room is not a square. The diagonal is too short for the room to be a square given the 17-inch wall.

The interest earned is approximately $50.06.

To calculate the amount of interest earned in a simple interest problem, we can use the formula:

[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{\text{Total days in a year}} \][/tex]

Given:

- Principal (P) = $1,295

- Rate (R) = 7% or 0.07

- Time (T) = 180 days

- Total days in a year = 365 days

Plugging these values into the formula:

[tex]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} \approx 1295 \times 0.07 \times 0.493150685 \]\[ \text{Interest} \approx 50.05958904 \][/tex]

Answer: 7/12 jar is full of marbles

Step-by-step explanation:

Matt had full Jar  of Marbles =  1

After giving 3/4 to Kayla , jar has marbles = [tex]1-\frac{3}{4}  \\=\frac{4}{4} -\frac{3}{4} \\=\frac{1}{4}[/tex]

Kayla returned  =   1/3 of Jar

Now jar has marbles =     1/3+ 1/4

                                 =   4/12 + 3/12     [ making denominator same]

                                 =  7/12

Answer:

152% of 72 = 109.44

Step-by-step explanation:

Answer:

All geometric figures, shapes and solids can be named as a sets of surface regions and plane regions and they all lie in three dimensional spaces.

Step-by-step explanation:

Step-by-step explanation:

Answer: Marco can fill 15 of the 2 1/2 Cups

Step-by-step explanation:

37.5 divided by 2.5

or

37 1/2 divided by 2 1/2

Answer:

Marco can fill 15 of the 2 1/2 Cups      

37 1/2 divided by 2 1/2

there are many combinations for it, but we can settle for say

[tex]\bf \begin{cases} f(x)=x+2\\[1em] g(x)=\cfrac{9}{x^2}\\[-0.5em] \hrulefill\\ (f\circ g)(x)\implies f(~~g(x)~~) \end{cases}\qquad \qquad f(~~g(x)~~)=[g(x)]+2 \\\\\\ f(~~g(x)~~)=\left[ \cfrac{9}{x^2} \right]+2\implies f(~~g(x)~~)=\cfrac{9}{x^2}+2[/tex]

Answer:

-96 or 96

Step-by-step explanation:

this is because the distance from zero is twelve, so it could be -12 or 12, plug both into the problem and then solve.

the absolute value |x| of a real number x is the non-negative value of x without regard to its sign.

|x| = x for x ≥ 0.

|x| = -x for x < 0.

Examples:

|2| = 2

|-5| = -(-5) = 5

If is -8 × |12| = -8 × 12 = -96

If is 8 × |12| = 8 × 12 = 96

Answer:

The inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].

Step-by-step explanation:

The given function is

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

The step and shown below to find the inverse of the function.

Step 1: Interchange x and y.

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

Step 2: Isolate variable y.

[tex]x-2=2y[/tex]

[tex]\frac{1}{2}(x-2)=y[/tex]

[tex]\frac{1}{2}(x)+\frac{1}{2}(-2)=y[/tex]

[tex]\frac{1}{2}(x)-1=y[/tex]

Therefore the  inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].

Answer:

The inverse of y = 2x+2 is 1/2x-1.

Step-by-step explanation:

Given equation is

y = 2x+2

let y = f(x) = 2x+2

We have to find the inverse of given function.

Adding -2 to both sides of given equation,we get

y-2 = 2x+2-2

y-2 = 2x

dividing by 2 to both sides of above equation , we have

(y-2) / 2 = 2x / 2

y/2 - 1 = x

Swapping equation, we have

x = y/2-1

put x = f⁻¹(y) in above equation ,we have

f⁻¹(y) = y/2 -1

Replace y with x , we have

f⁻¹(x) = x/2-1

Hence , the inverse of given function is 1/2x-1.

Answer:

17.922

Step-by-step explanation:

first you plug it in

y=0.860(17) + 3.302

then u simplify

y=14.62+3.302

then add them

y=17.922

Answer:

17.922 inches long

Step-by-step explanation:

y=0.860x + 3.302

y= 0.860(17) + 3.302

y= 14.62 + 3.302

y=  17.922

Hope it helps!!

Answer:

Step-by-step explanation:

f(12)=-2/3(12)+5

f(12)=-8+5

f(12)=-3

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

f(12) this means that x is 12, so you can plug in 12 for "x" in the function:

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

[tex]f(12)=-\frac{2}{3}(12)+5[/tex]

[tex]f(12)=-\frac{24}{3} +5[/tex]

f(12) = -8 + 5

f(12) = -3

Your answer is -3

Answer:

Linear

Step-by-step explanation:

y = 2^2

y = 4

This is a line.  4 is constant.  

Y to a constant value is a horizontal line

I'll do problem 77 to get you started

Point slope form is this general equation

y - y1 = m(x - x1)

with m as the slope and (x1,y1) as the point the line goes through. In this case, m = -4 and (x1,y1) = (-2,9)

Plug those values into the equation to get...

y - y1 = m(x - x1)

y - 9 = -4(x - (-2))

y - 9 = -4(x + 2) see note 1

y - 9 = -4x - 8

y = -4x - 8 + 9

y = -4x + 1 see note 2

--------

note 1: If your teacher wants the answer in point slope form, then you stop on this line. Otherwise, keep going

note 2: This is in slope intercept form y = mx+b with m = -4 as the slope and b = 1 as the y intercept

Final answer:

The multiplication of (3.4x10²) and (2x10³) results in 6.8x10⁵ after multiplying the coefficients and adding the exponents. Therefore, the correct answer is option (B).

Explanation:

Considering, the question it has asked to solve the following arithmetic operation in scientific notation: (3.4x10²)x(2x10³).

To solve this the following steps can be used :

we multiply the coefficients (3.4 and 2) and then add the exponents (2 and 3).

Multiplication of coefficients: 3.4 * 2 = 6.8

Addition of exponents: 2 + 3 = 5

Combining both parts: 6.8 x 10^5

The correct answer in scientific notation is therefore 6.8x10⁵, which corresponds with option B.

v=4/3 πr^3.

Use this formula

It could be possibly this

v=4/3 πr^3  

I hope it helped AND  I hope it's right,,

Hello from MrBillDoesMath!

Answer:

BC = 3 * sin (66)/ sin(38)

Discussion:

From the law of sines:

sin(38) /3 = sin(66)/ BC

BC *  (  sin(38)/3 )  = sin(66)        => multiply both sides by BC

BC = sin(66) /  ( sin(38)/3)           => multiply both sides by ( 3/sin(38) )

BC = 3 * sin (66)/ sin(38)

which is the first choice.

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

answer is A

Step-by-step explanation:..