199. By hand, find coordinates for the points where the line 3x + 2y
2-axis and the y-axis. These points are called the x-intercept and y-intercept, respectively.
Use these points to make a quick sketch of the line.

Answer:

\(\fbox{8a+10 = 6}\)

Step-by-step explanation:

\(2-3a =4+a\)

Adding 3a both side,

\(2 - \cancel{3a} + \cancel{3a} =4+a + 3a\)

\(2 = 4 + 4a\)

Subtracting 4 from both the side,

\(2 - 4 = \cancel4 - \cancel4 + 4a\)

\(4a = - 2\)

Now we have to find the value of 8a+10,

\(8a+10 = 2(4a) + 10\)

\(8a+10 = 2 \times ( - 2) + 10 \\ 8a+10 = - 4 + 10 \\ \fbox{8a+10 = 6}\)

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Hey! there

Answer:

Step-by-step explanation:

In this question we are given with an equation that is 2 - 3a = 4 + a . And we are asked to find the value of 8a + 10 .

So , for finding the value of 8a + 10 , we need to find the value of 'a' with the help of given equation.

\(\longmapsto \qquad \: \it{2 - 3a = 4 + a}\)

Step 1 : Adding '3a' on both sides :

\(\longmapsto \qquad \: \it{2 - \:\bold{ \cancel{3a}} + \bold{ \cancel{3a}} = 4 + \bold{a} + \bold{3a}}\)

On further solving,

\(\longmapsto \qquad \: \it{2 = 4 + 4a}\)

Step 2 : Subtracting with '2' on both sides :

\(\longmapsto \qquad \: \it{ \cancel{\bold{2 }} - \cancel{\bold{2 }}= \bold{ 4 }+ 4a - \bold{ 2}}\)

On further solving,

\(\longmapsto \qquad \: \it{0 = 2 + 4a}\)

Step 3 : Subtracting '4a' on both side s:

\(\longmapsto \qquad \: \it{0 - 4a= 2+ \cancel{\bold{4a}} - \cancel{\bold{4a}}}\)

On further solving,

\(\longmapsto \qquad \: \it{ - 4a= 2}\)

Step 4 : Dividing both sides by 4 :

\(\longmapsto \qquad \: \it{ \dfrac{ \cancel{- 4}a}{ \cancel{4}} = \cancel{ \dfrac{2}{4} }}\)

On further solving,

\(\longmapsto \qquad \: \it{ - a= \dfrac{1}{2} }\)

Step 5 : Multiplying both sides by '-1' :

\(\longmapsto \qquad \: \it{ - a \times (- 1)= \dfrac{1}{2} \times ( - 1) }\)

We get,

\(\longmapsto \qquad \: \it{ \boxed{\boxed{ \bold{a= - \dfrac{ 1}{2} }}}}\)

Now , substituting value of a in given expression that is 8a + 10 :

\( \longrightarrow \quad \: \frak{ \cancel{8} \times ( - \dfrac{1}{ \cancel{2}} ) + 10}\)

We get :

\(\longrightarrow \quad \: \frak{ 4 \times - 1 + 10}\)

\(\longrightarrow \quad \: \frak{ (- 4) + 10}\)

\(\longrightarrow \quad \: \frak{ \red{\underline{\red{\boxed{ 6}}}}} \quad \bigstar\)

Answer:

112÷7= 16 ounces per scoop.

160 ounces divided by 16 is 10 scoops

The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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Answer:

Parellel: y=-2x+17

Perpendicular: y=2x-3

Step-by-step explanation:

Hope this helps! ;-)

On solving the question, we can say that second function has vertical asymptote at x=2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.

The function that represents the graph is f(x) = 1/x-2 .

The graph of the function

From the given graph , the vertical asymptote is at x=2

Lets find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator =0

f(x) = 1/2x

2x = 0

x = 0

f(x) = 1/x-2

x-2 = 0

x = 2

The second function has vertical asymptote at x=2

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Answer:

For 6, the answer is, x= 65; alternate exterior angles theorem.

For 7, the answer is, x = 17; same-side interior angles postulate

Step-by-step explanation:

I don't have one sorry,

Step-by-step explanation:

x + y = 25

x - y = 13

x.y = ?

x + y = 25

y = 25 - x

x - y = 13

x - 25 + x = 13

2x = 13 + 25

2x = 38

x = 38/2

x = 19

y = 25 - x

y = 25 - 19

y = 6

(x, y) = (19,6)

So, find their product!!

= x.y

= 19 × 6

= 114

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

see the attachment photo!

Answer: The correct answer is 135 in².

Step-by-step explanation: An area of a polygon is this:

Area = (number of sides × length of one side × apothem)/2

(5 x 6 x 9) / 2 = 135

the length of the box is represented by (8m2)

does that mean 8m^2?

in English that would be 8 times m^2 or 8 * m * m.

if that is true, then the volume of the box would be equal to (8*m^2)^3 which is equal to 8^3 * m^6 which is then simplified further to 512 * m^6 which can also be written as 512m^6.

if we assume that m is 3, then the side of the box is equal to 8 * 9 which is equal to 72 and that is cubed to get 373248.

working that out algebraically, it would look like this:

(8*3^2)^3 equals 8^3 * (3^2)^3 which is equal to 8^3 * 3^6 which is equal to 512 * 729 which is equal to 373248

The simplified expression that represents the volume of the box is D. 512m.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.

The volume of a cube or a square box can be calculated by multiplying the length of one side by itself twice since all sides of a cube are equal. Therefore, the volume of the square wooden box in the question is:

Volume = (8m')³

= 8m' * 8m' * 8m'

= 64m' * 8m'

= 512m"³

So the simplified expression that represents the volume of the box is 512m"³. Both options C and D in the original question have the same answer, but there is a typo in option D where it only says "512m" instead of "512m³".

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Answer:

a) 7.5 meters b) 588.75

Step-by-step explanation:

To calculate the volume you need to multiply the 3 values together so

3x5x0.5 = 7.5

That is the volume

Then you got to multiply that by 78.50 to get the answer for b

78.50x7.5 =588.75

Answer:

$19.24

Step-by-step explanation:

Take 14.25 times 1.35.

The markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.

Barnes and Noble buy a book for $14.25. They mark up the price of the book by 35%.

As per the question, we have

cost = $14.25

markup rate = 35% = 0.35

Let's x represent markup for the book,

markup rate = markup/sale price × 100%

35% = x / $14.25

0.35 = x / $14.25

x = $14.25 × 0.35

Apply the multiplication operation, and we get

x = 4.9875

So sale price = markup + cost

So sale price = $4.9875 + $14.25

So sale price = $19.237

Thus, the markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

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The formula for half-life is:

where A is the amount of the substance after a certain time

A₀ = the initial value of the substance

e = the natural number with a value of 2.71828

k = decay rate

t = time

These are the given information in the question.

At t = 13 hrs, A₀ = 592, 032 grams, A = half of 592, 032 grams = 296, 016 grams.

At 52 hrs, A₀ = 592, 032 grams, A = ?

Before we can solve for the final value of the substance after 52 hrs, we need to solve for the decay rate "k" first. To solve that, let's use the information given at 13 hrs.

Solve for k. To do that, start dividing both sides by 592, 032.

Therefore, the decay rate of iodine is 0.053319 or -5.3319%

Now, let's apply this decay rate to solve for the final value of the substance after 52 hrs.

Solve for A.

Hence, after 52 hours, there is an approximate of 37, 002.03 grams of iodine left.

Answer:

1) y=x-4

2)y=x+2

Step-by-step explanation:

You can see on the first one y is just 4 less than x

You can see that the second one (graph) has a slope. As by the points, if you increase x by 0.5 you increase y by one.

Thus, y=x+2

Hope this helped! I can't see much of the question :)

Answer:

Step-by-step explanation:

fraction decomposition for the expression

13x - 7/(x+2)(4x-3)

Answer: A

Step-by-step explanation:

Step-by-step explanation:

To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due ($32,000)

- PMT is the monthly payment we want to find

- r is the annual interest rate (7.9%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**

Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

The solution to the trigonometric equation is sin( 6x ) = 2sin(3x)cos(3x)

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the equation be represented as A

Now , the value of A is

A = sin (6x)

From the trigonometric relations ,

The value of sin( 2x ) = 2sin(x)cos(x)

Now , when x is replaced by 6x

Substituting the values in the equation , we get

sin ( 6x ) = 2 sin ( 6x/2 ) cos ( 6x/2 )

On simplifying the equation , we get

sin ( 6x ) = 2 sin ( 3x ) cos ( 3x )

So , the value of the trigonometric relation is

sin(6x) = 2sin(3x)cos(3x)

Hence , the equation is sin(6x) = 2sin(3x)cos(3x)

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The possible lengths of the path are (2,3,5)

Any side of a triangle must be shorter than the other two sides added together. If a side is equal to the other two sides it is not a triangle.

Given here: A 9 mile long triangular path.

In Euclidean geometry, triangle inequlaity theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c.

Thus we have

a) 1+1=2<7 (False)

b)1+2=3<6 (False)

c)2+2=4<5 (False)

d) 2+3=5>4 ( True)

Therefore the possible lengths of the paths are (2,3,5)

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A triangular bike path is exactly  miles long. If each of the three connecting paths is a whole-number of miles long, which could be the lengths of the paths? (1 Point)

1mile,  1mile,  7miles

1 mile, 2 miles, 6 miles

2 miles,  2miles, 5 miles

2 miles,  3miles, 5 miles

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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The correct statements regarding the comparisons of the exponential functions are given as follows:

The definition of function f(x) is given as follows:

f(x) = 4(5)^x

Meaning that it has an y-intercept and an asymptote given as follows:

From the graph of function g(x), we have that:

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1. 4

2. less than

3. increase

4. negative

Got it right on Edmentum

Function f is represented by an equation in standard form with a = 4 and b = 5. This function is increasing and has a y-intercept of 4. The function approaches 0 as x approaches -∞ and approaches ∞ as x approaches ∞.

Function g crosses the y-axis at (0,5). The function approaches 2 as x approaches -∞ and approaches ∞ as x approaches ∞.

Because the y-intercept of function f is 4, it is less than the y-intercept of function g. Both functions increase on all intervals of x, but their end behavior is different as x approaches negative infinity.

Answer: y = – x – 6

y = x – 4

Substitute into y  = -x-6 into the second equation

y =x-4

-x-6 = x-4

Add x to each side

-x-6+x =x-4+x

-6 =2x-4

Add 4 to each side

-6+4 =2x-4+4

-2 = 2x

Divide by 2

-2/2 =2x/2

-1 = x

Now find y

y =-x-6

y = -(-1) -6

y =1-6

y = -5

Taking into account the zeros of a quadratic function, the time of the rocket when it is in the air is equal to 1.5 seconds.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

The zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

\(x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}\)

A rocket launched with height function h(t)= -16t²+ 24t

where

Time for which rocket is in the air given by h(t) = 0, so:

0= -16t²+ 24t

where:

Solving:

\(x1=\frac{-24+\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}\)

\(x1=\frac{-24+\sqrt{24^{2}} }{2x(-16)}\)

\(x1=\frac{-24+24 }{2x(-16)}\)

\(x1=\frac{0 }{-32}\)

x₁= 0

and

\(x2=\frac{-24-\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}\)

\(x2=\frac{-24-\sqrt{24^{2} } }{2x(-16)}\)

\(x2=\frac{-24-24}{2x(-16)}\)

\(x2=\frac{-48}{-32}\)

x₂= 1.5

Therefore, the time of the rocket in the air is 1.5 seconds.

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Answer:

Multiply 5 and 3 to get 15

15B4c

The area of the kite is A = 48 units²

Given data ,

Let the area of the kite be represented as A

Now , the value of A is

Let the first diagonal of the kite be d₁ = 12 units

Let the second diagonal of the kite be d₂ = 8 units

Now , Area of kite = ( 1/2 ) d₁ x d₂

On simplifying , we get

A = ( 1/2 ) ( 12 ) ( 8 )

A = 48 units²

Therefore , the value of A is A = 48 units²

Hence , the area of the kite is A = 48 units²

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Given the repeating decimal 0.155...

We will convert it to a fraction as follows:

so, the answer will be:

Answer:

X = 10

Z = 67

Step-by-step explanation:

We see that the angles are formed by the intersection of two lines.

Angles z and  67° are vertically opposite angles and therefore they are equal to each other

z°= 67°

Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°

z + 7x + 43 = 180

67 + 7x + 43 = 180

7x + 110 = 180

7x = 180 -110 = 70

x = 70/7 = 10

Answer:

\(\bf x+23=64\)

Step-by-step explanation:

you can try x+23=64

Let's solve it:-

\(\sf x+23=64\)

Subtract 23 from both sides:-

\(\sf x+23-23=64-23\)

\(\bf x=41\)

__________________

Hope this's what you're looking for!

Have a great day!

Answer:

How about this:

290 / 8 * 2 - 31.5

Step-by-step explanation:

I dunno if that's hard enough, but there you go!

Answer:

\(y = \frac{1}{4} x + 1\)

Step-by-step explanation:

He got the slope wrong and the y-intercepz wrong

Answer:

He is wrong. His slope is right but his y-intercept is wrong. He did -1 instead of +1.

Step-by-step explanation: