Find the difference (3•1,000)- (2•100)

To find the equation of a line in point-slope form, we need a point on the line and its slope. From the given options, we can see that the point in the graph is (600,500). Option A is the correct answer.

To find the equation of a line in point-slope form, we need a point on the line and its slope. From the given options, we can see that the point in the graph is (600,500). Now, we need to determine the slope of the line.
Looking at the graph, we can see that the line goes through the point (600,500) and another point (800,900). To find the slope, we can use the slope formula:
slope = (change in y)/(change in x)
slope = (900 - 500)/(800 - 600) = 400/200 = 2
Now, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1,y1) is the point (600,500) and m is the slope we just found.
Substituting the values, we get:
y - 500 = 2(x - 600)
Simplifying, we get:
y + 500 = 2(x - 600)
Therefore, option A is the correct answer.

To know more about point-slope visit :

https://brainly.com/question/8737935

#SPJ11

The functions that are exponential are f(x) = 4(1/4)ˣ , g(x) = 14(4)ˣ and k(x) = 6(5.49)ˣ , the options that are correct are (a) , (b) and (e) .

In the question ,

five function are given ,

we need to select the functions that are exponential ,

We know that , Exponential function is a function whose value is a constant raised to power of a variable ,

For Example , f(x) = cˣ, where c is any constant value and x is a variable.

Part(a) ,

f(x) = 4(1/4)ˣ

Since , x is in the exponent , hence it is an exponential function .

Part(b) ,

g(x) = 14(4)ˣ

Since , x is in the exponent , hence it is an exponential function .

Part(c) ,

h(x) = 10x⁵

Since , x is present in the base , hence , it is not an exponential function .

Part(d) ,

j(x) = −9x⁴

Since , x is present in the base , hence ,it is not an exponential function .

Part(e) ,

k(x) = 6(5.49)ˣ

Since , x is in the exponent , hence it is an exponential function .

Therefore , The exponential functions are (a) f(x) = 4(1/4)ˣ  , (b) g(x) = 14(4)ˣ   and  (e) k(x) = 6(5.49)ˣ  .

The given question is incomplete , the complete question is

which of the following are exponential functions? select all correct answers.

(a) f(x) = 4(1/4)ˣ

(b) g(x) = 14(4)ˣ

(c) h(x) = 10x⁵

(d) j(x) = −9x⁴

(e) k(x) = 6(5.49)ˣ

Learn more about Exponential Functions here

https://brainly.com/question/15909860

#SPJ4

Answer:

Step-by-step explanation:

Let the missing part be x.

According to triangle proportionality theorem we have:

The missing length will be 14 units.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown is figure.

Now,

Let the missing length = x

So, By the definition of triangle proportionality theorem, we get;

⇒ x/28 = 6 /(18 - 6)

Solve for x as;

⇒ x/28 = 6 /(18 - 6)

⇒ x/28 = 6 / 12

⇒ x/28 = 1 / 2

⇒ x = 28/2

⇒ x = 14

Thus, The missing length will be 14 units.

Learn more about the triangle visit:

https://brainly.com/question/23945265

#SPJ1

Answer:

Step-by-step explanation:

do I

Therefore, Don's car would use 67.035 L of gas to travel 735 km.

Cross multiplication is a method used to compare the relative sizes of two fractions. To cross-multiply two fractions, you multiply the numerator of one fraction by the denominator of the other fraction, and then do the same with the other numerator and denominator, putting the two products equal to each other. For example, if you have the fractions 2/3 and 3/4, you can cross-multiply as follows:

\(2/3 = x/4\)

\(2 x 4 = 3 x x\)

\(8 = 3x\)

\(x = 8/3\)

So, the two fractions are equivalent, and both are equal to 8/3. Cross-multiplication can also be used to solve equations that involve fractions, by isolating the variable on one side of the equation.

To find out how much gas Don's car would use to travel 735 km, we can use the fact that the car uses 9.1 L of gas every 100 km. We can set up a proportion to solve for the amount of gas used:

9.1 L / 100 km = x L / 735 km

To solve for x, we can cross-multiply and simplify:

\(9.1 L * 735 km = 100 km * x L\)

\(6703.5 Lkm = 100 km * x L\)

\(6703.5 Lkm / 100 km = x L\)

\(67.035 L = x L\)

To know more about equations, visit:

https://brainly.com/question/4280730

#SPJ1

The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

Learn more on the vectors here: https://brainly.com/question/2375446

#SPJ1

As cos(C) is negative, the triangle cannot be drawn with the given sides and angle. Hence, the given values do not result in a triangle.

Given that b = 5, c = 6, and B = 80°. We have to determine whether the given results are in one triangle, two triangles, or no triangle.

Therefore, let's find the value of the third angle of the triangle:

A + B + C = 180°

=> A = 180° - B - C

Substitute B = 80° in the above equation:

A = 180° - 80° - C

=> A = 100° - C

We have now found the value of all three angles of the triangle: A = 100° - C, B = 80°, and C = C

Substitute the values of sides and angles in the law of cosines to check whether the given sides and angles form a triangle. (A side of a triangle is opposite to its corresponding angle.)c² = a² + b² - 2ab cos(C)

Here, a is opposite to angle A, b is opposite to angle B, and c is opposite to angle C. Substitute the values of the given sides and angles in the above equation:

(6)² = a² + (5)² - 2(5)(a) cos( C )

=> 36 = a² + 25 - 10a cos( C )

=> a² - 10a cos( C ) - 11 = 0

Now substitute a = 2 in the above equation:

4 - 20 cos( C ) - 11 = 0

=> cos( C ) = -7/20

As cos(C) is negative, the triangle cannot be drawn with the given sides and angle. Hence, the given values do not result in a triangle. Therefore, the main answer is "no triangle".

To know more about the law of cosines, visit:

brainly.com/question/30766161

#SPJ11

Answer:

Here is the answer graphed:

The equation will be changed into = f(x)= 32

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

learn more about equations click here:

brainly.com/question/2972832

#SPJ1



Answer:

$16.10

Step-by-step explanation

14.00x .15=2.10

14.00+2.10=16.10

Answer:

x = 0

Step-by-step explanation:

-2(x-4)=4x+2x+8

Distribute

-2x +8 =4x+2x+8

Combine like terms

-2x+8 =6x+8

Add 2x to each side

-2x+2x+8 =6x+2x+8

8 = 8x+8

Subtract 8 from each side

8-8 = 8x+8-8

0 = 8x

Divide by 8

0=x

Answer:

x = 0

Step-by-step explanation:

-2(x-4) = 4x+2x+8

-2x+8 = 6x+8

8-8 = 6x+2x

0 = 8x

x = 0

Hope this will help and if so, then please mark me as brainliest.

Answer: n < -7 and n > -5

Step-by-step explanation:

-10|n+6| < -10

first divide by -10 on both sides

\(\frac{-10|n+6|}{-10}\) < \(\frac{-10}{-10}\)

since we are dividing, we have to flip the sign

|n+6| > 1

subtract the absolute value of 6

You are left with n < -7 and n > -5

Answer:

Step-by-step explanation:

1.Tan = opp/adj

Tan 45=x/8

Cross multiply

Tan 45 x 8 = x

1 x 8=x

X =8

2.sin=opp/hyp

Sin 45=8/y

Cross multiply

Sin45 x y =8

Divine both sides by sin45

Y = 8/sin 45

Y=8 ÷√2/2

Y=8 x 2/√2

Y=16/√2

Rationalise

Y= 16/√2 x√2/√2

Y=16√2/2

16 divided by 2 is 8

Y=8√2

Answer:  x = 8    y = 8√2

Step-by-step explanation:  If both angles are the same, 45°  the sides are the same, so  x = 8.

To find the hypotenuse, y, use the Pythagorean Theorem: a² + b² = c²

(In this question, c is y, and the x sides are a & b)

8² + 8² = y²   Here you can add the squares 66 + 64 = 128 and calculate the square root of 128  OR

(8²)(2) = y²     √(8²)(2) =  √y²  

8√2 = y

Average rate of change of \(y = x^2 + 4x - 1\\\) over the interval \(-4 \leq x \leq 1\)  is 1

What is average rate of change of a curve?

Average rate of change of a curve is equal to the slope of the curve and is obtained by dividing the change in functional value by the change in the value of the domain.

Here,

\(y = x^2 + 4x - 1\\\)

At x = -4,

\(y = (-4)^2+ 4(-4)-1\\y = -1\)

At x = 1

\(y = (1)^2 + 4(1) -1\\y = 4\)

Average rate of change of \(y = x^2 + 4x - 1\\\) over the interval \(-4 \leq x \leq 1\)

= \(\frac{4 - (-1)}{1- (-4)}\\\\\\\frac{5}{5}\\\\1\)

To learn more about average rate of change, refer to the link -

https://brainly.com/question/8728504

#SPJ1

If the conditions for a binomial distribution are met, the variance, given the number of trials (n) and the probability of success(p) is given as:

Given:

n = 170

p = 0.7

Solution

By substituting the given values, the variance is:

Answer: 35.7

Answer:

With the assumption that the line FD passes through the point B, we have;

y = 7

x = 6

Step-by-step explanation:

The given parameters are;

Line FD bisects segment AC

Therefore, segment AE = segment EC By definition of line AC which is bisected by the line FD

Segment ED ≅ Segment ED by reflexive property

∠CED = ∠AED = 90° (Angles formed by a perpendicular bisector (FD) to a line (AC))

Therefore;

ΔCDE ≅ ΔADE by Side-Angle-Side (SAS) rule of congruency

From which we have;

Segment CD ≅ Segment AD Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Segment CD = Segment AD Definition of congruency

∴ 12·y - 8 = 8·y + 20 by substitution property

12·y - 8·y = 20 + 8

4·y = 28

y = 28/4 = 7

y = 7

From segment AE = segment EC, we have;

2·x + 4·y = 2·x + 4·y by substitution property

2·x + 4×7 = 2·x + 4×7 by substitution property

Segment AE = 2·x + 28 = Segment EC

Segment AC = Segment AE + Segment EC by definition of segment (AC) bisected by a line (FD)

∴ Segment AC = 2·x + 28 + 2·x + 28 = 4·x + 56 by substitution property

Segment CD = 8·y + 20 = 8 × 7 + 20 = 56 + 20 = 76

Segment CD = 76

The sides of the ΔABC are;

Segment BC = 6·x + 18

Segment BA = 8·x + 6

Segment AC = 4·x + 56

With the assumption that the Line FD passes through the point B, we have;

Segment BC = Segment AB by congruent triangles ΔABE ≅CBE based on Side-Angle-Side (SAS) rule of congruency

Therefore;

6·x + 18 = 8·x + 6

18 - 6= 8·x - 6·x = 2·x

2·x = 18 - 6 = 12

x = 12/2 = 6

x = 6

Answer: NA and Rb and there are 20 protons in calcium!

Step-by-step explanation:

Answer:

No. of protons = 20

No. of electrons = 20

No. of neutrons = 20

Step-by-step explanation:

Part 1 :

Na, K and Rb are in the same group.

So, K and Rb are the two elements that have the same properties as sodium ( Na ).

Part 2 :

Atomic Number of Calcium = 20

Note :

Atomic Number = No. of protons

Therefore,

No. of protons = 20

Note :

No. of neutrons = No. of protons.

Therefore,

No. of neutrons = 20

Calcium is the 20th element, with 20 protons. Since a stable atom has a net charge of 0, it must have 20 electrons.

Answer:

there is no number that can do that the closest you can get is 7 and 7 giving you 49 when multplied

Step-by-step explanation:

Answer:

10 × 2 × 2 = 50

10 + 2 + 2 = 14

The probability that one of the pulled cards is double the value of the other is 0.0101.

Consider the possibility of the first card being double or the second card being doubled. There are 50 possible combinations if the first card is doubled. When the first card is double, the second card has a 1/99 chance of being the half-card

The probability of the first card being doubled is as follows:

= 50 × 1/100 × 1/99

So the probability of drawing two cards, where one is double the other, is:

= 2 × 1/2 × 1/99 or 0.0101

To Learn more about probability of drawing cards Question:

https://brainly.com/question/23275510

#SPJ4

The missing statement in Step 5 include the following: B. AC/DC = BC/EC.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the angle, angle (AA) similarity theorem, we can logically deduce the following congruent triangles:

ΔABC ≅ ΔDEC  ⇒ Step 4

By the definition of similar triangles, we can logically deduce the following proportional and corresponding side lengths:

AC/DC = BC/EC ⇒ Step 5

Read more on triangles here: https://brainly.com/question/11763540

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x=-2

Step-by-step explanation:

first, remove the parenthesis.

3x-2x+1=7x-3+5x-x+24

collect like terms

x+1=11x+21

subtract x from both sides

1=10x+21

subtract 21 from both sides

-20=10x

divide both sides by 10

-2=x

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

Answer:

S∞=12. Explanation: Formula for sum of infinite geometric series is. S∞=a11−r ; −1<r<1. We have a geometric series ...

Step-by-step explanation:

That's it hope it helps.^^

#carryonlearning

The application of the identity tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)).the result tan(2x) = 2*tan(x)/(1 - tan²(x)).

Statement | Reason

Tangent (2x) | Given= tangent (x + x) | 1= startfraction tangent (x) + tangent (x) over 1 minus tangent (x) tangent (x) endfraction | 2= startfraction 2 tangent (x) over 1 minus tangent squared (x) endfraction | 3.Reason 1 is the application of the identity tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)). Reason 2 is the application of the identity tan(2x) = 2*tan(x)/(1 - tan²(x)). Reason 3 is the result of the two previous steps, which is the solution to tan(2x). By applying the identities, we have derived the result tan(2x) = 2*tan(x)/(1 - tan²(x)).

Learn about tangent here:

https://brainly.com/question/19064965

#SPJ4

Answer:

Reason 1 is - Addition

Reason 2 is - Tangent Sum Identity

Reason 3 is - Simplify

Step-by-step explanation:

edge

1. The terminal point P(x, y) determined by a real number t is given. So, the answer is sin t = 3/5, cos t = 4/5, and tan t = 3/4.

We need to first determine the values of x and y in order to find sin t, cos t, and tan t. We are given the point P(x, y) = (4/5, 3/5), which is centered on the unit circle.

We can use the Pythagorean theorem to find the value of the radius r of the unit circle:

r = √(x² + y²)

= √(4/5)² + (3/5)²)

= √(16/25 + 9/25)

r = √(25/25)

r = 1

So the point P lies on the unit circle, and its coordinates satisfy x = 4/5 and y = 3/5.

Now, we can use the definitions of sin t, cos t, and tan t to find their values:

sin t = y/r = (3/5) / 1 = 3/5

cos t = x/r = (4/5) / 1 = 4/5

tan t = y/x = (3/5) / (4/5) = 3/4

Therefore, sin t = 3/5, cos t = 4/5, and tan t = 3/4.

2. The terminal point P(x, y) determined by a real number t is given. So, the answer is sin t = (√15)/8, cos t = -7/8, and tan t = -(√15)/7

We need to first determine the values of x and y in order to find sin t, cos t, and tan t. The point P(x, y) = (-7/8, (√15/8) on the unit circle centered at the origin is provided to us.

We can use the Pythagorean theorem to find the value of the radius r of the unit circle:

r = √(x² + y²)

= √(-7/8)² + (√15)/8)²

= √(49/64 + 15/64)

r = √(64/64) = 1

r = 1

So the point P lies on the unit circle, and its coordinates satisfy x = -7/8 and y = √15/8.

Now, we can use the definitions of sin t, cos t, and tan t to find their values:

sin t = y/r = (√15)/8) / 1 = √15/8

cos t = x/r = (-7/8) / 1 = -7/8

tan t = y/x = (√15)/8) / (-7/8) = -(√15)/7

Therefore, sin t = (√15)/8, cos t = -7/8, and tan t = -(√15)/7.

3. The values of the trigonometric functions of t from the given information. tan t= (-5/12) cos t > 0. So, the answer is sin t = 12/13 , cos t = -5/13

We know that tan t = (-5/12) cos t > 0. We know that t must be in the second quadrant since tan t is negative in the second and fourth quadrants and cos t is negative in the second and third quadrants. Cosine is negative in the second quadrant, while sine is positive. The Pythagorean identity may be used to calculate the value of sin t:

sin² t + cos² t = 1

sin² t + (-5/12)² sin² t = 1

(1 + 25/144) sin² t = 1

169/144 sin² t = 1

sin² t = 144/169

sin t = √(144/169) = 12/13

Now, we can find the cos t:

cos t = -√(1 - sin² t)

= -√(1 - (144/169))

cos t= -5/13

Therefore, sin t = 12/13 , cos t = -5/13

Learn more about Pythagorean theorem:

https://brainly.com/question/14669175

The correct question:

#SPJ4