Write an exponential function whose graph contains the points (1, 6) and (0, 2).

ANSWER

The standard form is:

[tex]x - 2y = - 16[/tex]

EXPLANATION

The given line passes through (4,10)and (6,11).

The slope of this line is

[tex]m = \frac{11 - 10}{6 - 4} [/tex]

[tex]m = \frac{1}{2} [/tex]

The equation is given by the formula,

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

We plug in the first point and the slope to get.

[tex]y-10= \frac{1}{2} (x-4)[/tex]

[tex]2y - 20 = x - 4[/tex]

[tex]x - 2y = - 20 + 4[/tex]

[tex]x - 2y = - 16[/tex]

The standard form is

[tex]x - 2y = - 16[/tex]

Give me BRAINLIEST please

let's say the total holdings for the company, or namely the total quantity for the ratios is say hmmm "x", and we were to split "x" in quantities of 27:19:14:11 ratio, what we do is, we simply divide "x" by (27+19+14+11), and then distribute accordingly.

so, if we divide the total amount like that, we end up with fragments of the total, and each ratio gets so many fragments.

so, we know the German stock or that ratio gets $238 millions, and in those 238, since it's on a 14 ratio, there are 14 of those fragments of the total, how much is a fragment anyway?  well, simply how many times does 14 go into 238?  238 ÷ 14 = 17.

well, since we know the whole total of the holdings was split in fragments of 17, let's simply distribute accordingly.

[tex]\bf \stackrel{American}{27(17)}~~:~~\stackrel{Japanese}{19(17)}~~:~~\stackrel{German}{14(17)}~~:~~\stackrel{British}{11(17)} \\\\\\ \stackrel{American}{459}~~:~~\stackrel{Japanese}{323}~~:~~\stackrel{German}{238}~~:~~\stackrel{British}{187}\qquad \textit{in millions}[/tex]

Answer:

9

Step-by-step explanation:

It is congruent to the other side.

Answer:

2/5

Step-by-step explanation:

Rise over run

Difference of y over the difference in x

Answer:

The slope is 2/5

Step-by-step explanation:

The slope formula is delta y over delta x.  If you insert the coordinates the equation is 1-3 / 3-8 = -2/-5 = 2/5.  The slope is 2/5

The answer is:

2. A point halfway between the endpoints of a line segment.

The midpoint of a line segment, is a point that divides the line segment into two equal length sides, no matter the length of the segment, the midpoint will always cut the segment into two equal length sides

The midpoint is an ordinary point located in the middle of the line segment. The x-coordinate of the midpoint is halfway between the x-coordinates of the beginning and the end of the segment. The y-coordinate of the midpoint is halfway between the y-coordinates of the beginning and the end of the segment.

Hence, the correct option is:

2. A point halfway between the endpoints of a line segment.

Have a nice day!

Midpoint refers to point in the mid. The midpoint of a line segment is given as: Option 2: A point halfway between the endpoints of a line segment.

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

If you walk halfway between the endpoints of a line segment, you'll reach to its mid, and thus, the midpoint of a line segment can be reached by walking halfway between its end points.

Thus,

The midpoint of a line segment is given as: Option 2: A point halfway between the endpoints of a line segment.

Learn more about midpoint of line segment here:

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Answer:

y = 2x - 10

Step-by-step explanation:

First, we find the slope.

m = slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(4 - 7) = -6/(-3) = 2

Now we use the slope in the slope-intercept form of the equation of a line.

y = mx + b

y = 2x + b

We use the coordinates of one of the given points for x and y, and we solve for b. Let's use the point (7, 4), so we have x = 7 and y = 4.

4 = 2(7) + b

4 = 14 + b

Subtract 14 from both sides.

-10 = b

Now we replace b with -10.

y = 2x - 10

Answer: y = 2x - 10

Answer:

15 x - 35 x y

Step-by-step explanation:

5 x (3-7 y)

5 * 3 x - 7 * 5 x y

= 15 x - 35 x y

A = base x height

A = (3/5 - 1/5) x 2/5

A = 2/5 x 2/5

A = (2/5)²

A = 2²/5²

A = 4/25

The answer is D) 4/25 square feet.

Answer:

can you help me with my answer when your done on my page? vvvvv

Step-by-step explanation:

1. **Separating 90 into Two Parts:**

  - The smaller part is [tex]\( 18 \)[/tex] and the larger part is [tex]\( 72 \)[/tex].

2. **Sum of Three Consecutive Integers:**

  - The three integers (in order) are [tex]\( 17, 18, \)[/tex] and [tex]\( 19 \)[/tex].

1. **Separating 90 into Two Parts:**

  - Let's denote the smaller part as [tex]\( x \)[/tex] and the larger part as [tex]\( 4x \)[/tex].

  - According to the problem, the sum of these two parts equals 90: [tex]\( x + 4x = 90 \)[/tex].

  - Combine like terms: [tex]\( 5x = 90 \)[/tex].

  - Divide both sides by 5 to solve for [tex]\( x \): \( x = 18 \)[/tex].

  - So, the smaller part is [tex]\( 18 \)[/tex] and the larger part is [tex]\( 4 \times 18 = 72 \)[/tex].

2. **Sum of Three Consecutive Integers:**

  - Let's denote the smallest integer as [tex]\( x \)[/tex].

  - The next two consecutive integers would be [tex]\( x + 1 \)[/tex] and [tex]\( x + 2 \)[/tex].

  - According to the problem, the sum of these three integers equals 54: [tex]\( x + (x + 1) + (x + 2) = 54 \)[/tex].

  - Combine like terms: [tex]\( 3x + 3 = 54 \)[/tex].

  - Subtract 3 from both sides: [tex]\( 3x = 51 \)[/tex].

  - Divide both sides by 3 to solve for [tex]\( x \): \( x = 17 \)[/tex].

  - So, the three consecutive integers are [tex]\( 17, 18, \)[/tex] and [tex]\( 19 \)[/tex].

The complete question is here:

Separate 90 into two parts so that one part is four times the other part. What are the sizes of the two parts? The smaller part is _____ and the larger part is ____.

The sum of three consecutive integers is 54. Find the three integers. The three integers (in order) are ____, ____, and ____.

Answer:

39

Step-by-step explanation:

5x - 1 when x = 8

plug the variable in

5(8) - 1

40 -1

39

Answer:

39

Step-by-step explanation:

5(8) is 40, minus one is 39.

Answer:

Step-by-step explanation:

To move the graph 6 units to the right, subtract 6 in the absolute value.

y=|x+5-6|

To move it up, add 2 outside the absolute value.

y=|x+5-6|+2

Now remove the absolute values since x>1.

y=x+5-6+2

y=x+1

Answer:

12y

Step-by-step explanation:

28y - 16y

Factor out a y

y(28-16)

y(12)

The difference is 12y

Answer:

B) Distribute 1.2 to 6.3 and –7x

D) Combine 3.5 and 7.56

E) Subtract 11.06 from both sides

Answer:

b, d, and e :)

Answer:

[tex]500\ cm[/tex]

Step-by-step explanation:

step 1

Find the volume of hollow cylinder

[tex]V=\pi (r2^{2}-r1^{2})h[/tex]

we have

[tex]r2=8\ cm[/tex]

[tex]r1=6\ cm[/tex]

[tex]h=35\ cm[/tex]

substitute

[tex]V=\pi (8^{2}-6^{2})(35)[/tex]

[tex]V=\pi (28)(35)[/tex]

[tex]V=980\pi\ cm^{3}[/tex]

step 2

we know that

The wire is a solid cylinder with the same volume of the hollow cylinder

so

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=980\pi\ cm^{3}[/tex]

[tex]r=2.8/2=1.4\ cm[/tex] ----> the radius is half the diameter (thickness)

substitute and solve for h

[tex]980\pi=\pi (1.4)^{2}h[/tex]

[tex]980=(1.96)h[/tex]

[tex]h=980/(1.96)=500\ cm[/tex]

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\\d=3\\a_n=99\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=3+(n-1)\cdot 3\\3n-3=96\\3n=99\\n=33\\\\S_{33}=\dfrac{3+99}{2}\cdot33=51\cdot33=1683[/tex]

Answer:

(1,2)  maximum

Step-by-step explanation:

The vertex is the the point on the graph where the graph does a "u-turn".

this point can either represent the maximum value or the minimum value depending on which way the graph is facing.

In this case, the graph looks like an "n" (as opposed to a "u").

We can clearly see that the point where the graph makes a U-turn is (1, 2)

we can also see that no part of the graph extends above this point, hence this point represents the maximum value which y could possibly be.

Hence (1,2) is maximum

Rewrite 100  as  10 ^2 .  x^ 2  −  10 ^2

Since both terms are perfect squares, factor using the difference of squares formula,  a^2 -b^2= (a + b) (a - b) where a = x and b = 10.

(x + 10) (x - 10)

Answer:

He is incorrect because the scale factor is 1/3.

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Triangles CA'B' and CAB are similar

The pre-image is the triangle CAB

The image is the triangle CA'B'

therefore

The scale factor is equal to

CB'/CB

we have

CB'=2 units

CB=2+4=6 units

substitute

CB'/CB=2/6=1/3

therefore

He is incorrect because the scale factor is 1/3.

[tex]\bf \begin{array}{ccll} \stackrel{x}{\textit{sprayed times}}&\stackrel{f(x)}{\textit{left termites}}\\ \cline{1-2} 1&12000\left( \frac{1}{4} \right)^1\\\\ 2&12000\left( \frac{1}{4} \right)^2\\\\ 3&12000\left( \frac{1}{4} \right)^3\\\\ x&12000\left( \frac{1}{4} \right)^x\\ \end{array}[/tex]

Answer:

the answer is C

Step-by-step explanation:

Answer:

20/3 or 6 2/3

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer: 28/3

7/3 x 4

=28/4

= 9&1/3

Answer:

75 degrees

Step-by-step explanation:

This is because all the angles in a triangle are supplementary which means they add up to 180 degrees.   This means that you subtract 180 from the other two angles

Please give Brainliest!!! Thanks! :D

Answer:

C. 75 degrees

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

You already know the degree of two angles: 70 & 35.

Now, subtract those numbers from 180 to find the degree of the missing angle.

180 - 70 - 35 = 75

So, the answer is C. 75 degrees.

I hope this helps!

Answer:

Option A. x=30,y=42

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and ZYX have three congruent interior angles

therefore

Triangles are similar

step 1

Find the value of x

[tex]\frac{ZY}{AB}=\frac{ZX}{AC}[/tex]

substitute the values

[tex]\frac{20}{x}=\frac{12}{18}[/tex]

[tex]x=20*18/12=30\ units[/tex]

step 2

Find the value of y

[tex]\frac{ZY}{AB}=\frac{XY}{CB}[/tex]

substitute the values

[tex]\frac{20}{30}=\frac{28}{y}[/tex]

[tex]y=30*28/20=42\ units[/tex]

Answer:

Part A) [tex]sin(2\theta)=\frac{24}{25}[/tex]

Part B) [tex]cos(2\theta)=0[/tex]

Part C) [tex]tan(2\theta)=-\frac{240}{161}[/tex]

Step-by-step explanation:

Part A) we have [tex]cos(\theta)=-\frac{4}{5}[/tex]

θ is in quadrant 3 ----> the sine is negative

Find [tex]sin(2\theta)[/tex]

we know that

[tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]

Remember that

[tex]cos^{2} (\theta)+sin^{2} (\theta)=1[/tex]

substitute

[tex](-\frac{4}{5})^{2}+sin^{2} (\theta)=1[/tex]

[tex](\frac{16}{25})+sin^{2} (\theta)=1[/tex]

[tex]sin^{2} (\theta)=1-\frac{16}{25}[/tex]

[tex]sin^{2} (\theta)=\frac{9}{25}[/tex]

[tex]sin(\theta)=-\frac{3}{5}[/tex] ---> remember that the sine is negative (3 quadrant)

Find [tex]sin(2\theta)[/tex]

we have

[tex]cos(\theta)=-\frac{4}{5}[/tex]

[tex]sin(\theta)=-\frac{3}{5}[/tex]

[tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]

substitute

[tex]sin(2\theta)=2(-\frac{3}{5})(-\frac{4}{5})[/tex]

[tex]sin(2\theta)=\frac{24}{25}[/tex]

Part B) we have [tex]cos(\theta)=\frac{\sqrt{2}}{2}[/tex]

θ is in quadrant 1

Find [tex]cos(2\theta)[/tex]      

we know that

[tex]cos(2\theta)=2cos^{2} (\theta)-1[/tex]

substitute

[tex]cos(2\theta)=2(\frac{\sqrt{2}}{2} )^{2}-1[/tex]

[tex]cos(2\theta)=0[/tex]

Part C) we have [tex]sin(\theta)=\frac{8}{17}[/tex]

θ is in quadrant 2 ----> the cosine is negative

Find [tex]tan(2\theta)[/tex]  

we know that

[tex]tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}[/tex]

Remember that

[tex]cos^{2} (\theta)+sin^{2} (\theta)=1[/tex]

substitute

[tex]cos^{2} (\theta)+(\frac{8}{17})^{2}=1[/tex]

[tex]cos^{2} (\theta)=1-\frac{64}{289}[/tex]

[tex]cos^{2} (\theta)=\frac{225}{289}[/tex]

[tex]cos(\theta)=-\frac{15}{17}[/tex]

Find [tex]tan(\theta)[/tex]  

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

substitute

[tex]tan(\theta)=\frac{(8/17)}{(-15/17)}[/tex]

[tex]tan(\theta)=-\frac{8}{15}[/tex]

Find [tex]tan(2\theta)[/tex]  

[tex]tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}[/tex]

substitute

[tex]tan(2\theta)=\frac{2(-\frac{8}{15})}{1-(-\frac{8}{15})^{2}}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{1-(\frac{64}{225})}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{1-\frac{64}{225}}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{\frac{161}{225}}[/tex]

[tex]tan(2\theta)=-\frac{240}{161}[/tex]

i think the answer to this question would be 1

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{x-intercept:}\ (x,\ 0).\\\\\text{Susbtitute the coordinates of the points to the formula of a slope}\\\\(-3,\ -4),\ (6,\ 2),\ (x,\ 0):\\\\m=\dfrac{2-(-4)}{6-(-3)}=\dfrac{2+4}{6+3}=\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\\\\m=\dfrac{0-2}{x-6}=\dfrac{-2}{x-6}\\\\\text{Therefore we have the equation:}\\\\\dfrac{-2}{x-6}=\dfrac{2}{3}\qquad\text{cross multiply}\\\\2(x-6)=(-2)(3)\\\\2(x-6)=-6\qquad\text{divide both sides by 2}\\\\x-6=-3\qquad\text{add 6 to both sides}\\\\x=3[/tex]

[tex]\bold{METHOD\ 2}\\\\\text{Look at the picture.}[/tex]

Mark points in the coordinate system.

Lead a line through these points.

Read x-intercept.

Answer: the answer is D

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

No values of x exist that make the equation true

Answer:

There are no solutions

Step-by-step explanation:

-7x-10-15x=-22x+83

Combine like terms

-22x -10 = -22x +83

Add 22x to each side

-22x +22x-10 = -22x+22x +83

-10 = 83

This is never true so there are no solutions

Answer:

1 5/7 bags of flour to make three batches of cookies

Step-by-step explanatio

12/7 bag of the flour is required to make 3 batches of cookies

Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of the symbols that is split in to left or right sides joined by the equal sign. For example, 2 + 4 + 5 = 11 is an equation.

When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which is assumed to be known, is usually known as constants, coefficients and parameters

From the question;

2/7 bag of flour makes 1/2 of a batch of cookies

x bag of flour will make 3 batches of cookies

Mathematically, we cross multiply

2/7 * 3 = 1/2 * x

6/7 = x/2

2 * 6 = 7 * x

12 = 7x

x = 12/7 bag of flour

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#SPJ2

Answer:

y = - 5 x + 6

Step-by-step explanation:

to be parallel it will have the same slope and you solve for b by making a new equation

y = - 5 x  + b

and plugging in the x and y values from your coordinate point in for x and y

you then solve for b which will be 6 and you form the equation

Answer:

Y = -5x +12

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

f(x)=-2(x+3)^2-5

The equation is in the form

f(x) = a(x-h)^2 -k

where (h,k) is the vertex

The h value is also the axis of symmetry

f(x)=-2(x--3)^2-5

The vertex is (-3,-5)

so the axis of symmetry is x=-3