A line passes through (−1, 7) and (2, 10) what is the equation of the line?

Answer:

$1475.40

Step-by-step explanation:

Since the interest is two times per year for 5 years, do this 10 times:

1) 750*0.07=52.5

750+52.5=802.5

2) 802.5*0.07=56.18

802.5+56.18=858.69

3) 858.69*0.07=60.11

858.69+60.11=918.79

4) 918.79*0.07=64.32

918.79+64.32=983.11

5) 983.11*0.07=68.82

983.11+68.82=1051.93

6) 1051.93*0.07=73.64

1051.93+73.64=1125.57

7) 1125.57*0.07=78.79

1125.57+78.79=1204.36

8) 1204.36*0.07=84.31

1204.36+84.31=1288.67

9) 1288.67*0.07=90.21

1288.67+90.21=1378.88

10) 1378.88*0.07=96.52

1378.88+96.52=1475.40

Answer:

1

Step-by-step explanation:

The line in the graph has a slope of -1. The slopes of lines that are perpendicular have a product of -1 so the answer is 1.

Answer: -4

Step-by-step explanation:

Do -6 x 2 to get -12, then divide by 3 to get -4

Thats assuming this is a fraction and not an actual division sign

Answer:

Average speed of boat = 3.67 km/h

Average speed of stream = 0.63 km/h

Step-by-step explanation:

30 km upstream in 10 hours gives a speed of 30/10 = 3 km/h relative speed of boat and stream

Same way, 44 km in 10 hrs = 4.4 km/h relative speed of boat and stream.

Let the speed of the stream be y

Let the speed of both be x, then

x - y = 3.... (1)

x + y = 4.4.... (2)

Subtract 1 from 2

2y = 1.4

y = 1.4/2 = 0.7 km/h

substitute value of y in 1

x - 0.7 = 3

x = 3.7 km/h

Also, 40 km upstream in 13 hrs gives speed of 3.08 km/h

55 km in 13 hrs gives 4.2 km/h

Let speed of boat be x and that of stream be y

x - y = 3.08.... (1)

x + y = 4.2..... (2)

Subtract 1 from 2

2y = 1. 12

y = 0.56 km/h

Substitute value of y in 1

x - 0.56 = 3.08

x = 3.64 km/h

Average speed of boat = (3.7 + 3.64)/2

= 3.67 km/h.

Average speed of stream = (0.7 + 0.56)/2 = 0.63 km/h

Answer:

As we know that,

[tex]\bigstar \: \: \sf Time = \dfrac{Distance}{Speed} \\ \\ [/tex]

[tex]\bigstar\:\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\[tex]

[tex]:\implies \sf \dfrac{30}{x - y} + \dfrac{44}{x + y} = 10 \\ \\ \\ [/tex]

[tex]:\implies \sf \dfrac{40}{x - y} + \dfrac{55}{x + y} = 13 \\ \\ \\[/tex]

[tex]\sf Let \: \dfrac{1}{x - y} = \textsf{\textbf{m}} \sf \: \: and \: \: \sf{\dfrac{1}{x + y} = \textsf{\textbf{n} }}\\ \\ \\[/tex]

[tex]:\implies \sf 30m + 44n = 10\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (i)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]:\implies \sf 40m + 55n = 13\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (ii)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny \underline{\frak{ Multiply \: equation \: (ii) \: by \: 3 \: and \: equation \: (i) \: by \: 4 :}} \\[/tex]

[tex]:\implies \sf 120m + 176n = 40\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iii)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]:\implies \sf 120m + 165n = 39\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iv)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny \underline{\frak{ Substracting \: equation \: (iii) \: from \: equation \: (iv) \: we \: get :}} \\[/tex]

[tex]\sf 120m + 176n = 40 \\ \\

\sf 120m + 165n = 39 \\ \\ [/tex]

[tex]\sf \: \: ( - ) \:\:\: \: \: ( - ) \: \: \: \: \: \: \: ( - ) [/tex]

_____________________

[tex]\: \: \: \: \qquad\sf 11n= 1 \\[/tex]

[tex]\: \: \: \: \: \qquad\sf n= \dfrac{1}{11} \\ \\ [/tex]

[tex]\qquad\tiny {\frak{ Put\: n = \dfrac{1}{11}\:in\:equation \: (i) \: we \: get :}} \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m + 44 \times \dfrac{1}{11} = 10 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m= 10 - 4 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m= 6 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf m= \dfrac{6}{30} \\ \\ \\ [/tex]

[tex]\dashrightarrow\:\:\sf m= \dfrac{1}{5} \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf \dfrac{1}{x - y} = m\\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf x - y= 5\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (v)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf \dfrac{1}{x + y} = n\\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf x + y= 11\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (vi)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny {\frak{Adding\:equation \: (v) \: and \: equation \: (vi) \: we \: get :}} \\[/tex]

[tex]:\implies \sf 2x = 16 \\ \\ \\[/tex]

[tex]:\implies \underline{ \boxed{ \textsf {\textbf{x = 8 km/hr}}}} \\ \\[/tex]

[tex]\qquad\tiny {\frak{Putting\:x = 8\: in \: equation \: (v) \: we \: get :}} \\[/tex]

[tex]:\implies \sf 8 - y = 5 \\ \\ \\ [/tex]

[tex]:\implies \sf y = 8 - 5 \\ \\ \\[/tex]

[tex]:\implies \underline{ \boxed{ \textsf {\textbf{y = 3 km/hr}}}} \\ \\[/tex]

[tex]\bigstar\:\underline{\sf{Therefore\: speed\: of \:boat\: in\: still \:water\: and\: speed\: of\: stream:}} \\[/tex]

[tex]\bullet\:\:\textsf{Speed of boat in stream = \textbf{8 km/hr}}\\[/tex]

[tex]\bullet\:\:\textsf{Speed of boat in still water = \textbf{3 km/hr}}\\[/tex]

Answer:

D

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

→Distribute the -1 to (x - 1):

(x - 5) - (x - 1)

x - 5 - x + 1

→Add like terms (x and -x, -5 and 1):

-4

Answer:

-4

Step-by-step explanation:

(x-5)-(x-1)

x-5-x+1

x-x-5+1 = -4

Answer:

-15

Step-by-step explanation:

g(-1) = -2(-1)^2 -4 = -2 *1 -4 = -6

f(-2) = (-2)^2 -3 = 4 -3 = 1

3* [g(-1)+ f(-2) ]

3( -6+1)

3 ( -5)

-15

Answer:

3 acute angles with different measures and 1 right angle and 2 acute angles with same measures

Answer:

the set of all the real values which are strictly greater than zero which is all positive real numbers

Step-by-step explanation:

In interval notation: (0, ∞)

Any exponential function with a positive base and positive multiplier will have a horizontal asymptote at y=0 and will extend to +∞. That's what this one does.

Range of a function--

The range of a function is the set of all the values that are attained by a function.

We are asked to find the range of the function f(x)

the set of all the real values which are strictly greater than zero

x > 0

please mark me brainliest :)

Answer:

115

Step-by-step explanation:

When two angles are supplementary, their measures must add up to 180 degrees. Therefore, if we call the other angle x:

x+65=180

x=180-65=115 degrees

Hope this helps!

Answer:

None of them

Step-by-step explanation:

Supplementary angles have 180 degrees

50+65=115

40+65=105

130+65=185

310+65=375

Answer:

50 quarts

Step-by-step explanation:

64oz*25=1600oz

1600oz/32=50q

(32oz in each quart)

Answer:

0.2924

Step-by-step explanation:

Use a calculator.

cos 73 deg = 0.2924

Answer:

  b.  4.0 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the ratio of the adjacent side to the hypotenuse is given by the cosine of the angle:

  Cos = Adjacent/Hypotenuse

  cos(35°) = NL/NK

  NL = NK·cos(35°)

__

Similarly, it reminds you that the ratio of the opposite side to the hypotenuse is given by the sine function:

  Sin = Opposite/Hypotenuse

  sin(53°) = NM/NL

  NM = NL·sin(53°)

Substituting from the first triangle, we have ...

  NM = NK·cos(35°)·sin(53°)

  NM = (6.1 cm)(0.81915)(0.79864)

  NM ≈ 3.991 cm

  MN ≈ 4.0 cm

Answer:

gradient = 4

Step-by-step explanation:

Calculate the gradient using the slope formula

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

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 14)

m = [tex]\frac{14-2}{3-0}[/tex] = [tex]\frac{12}{3}[/tex] = 4

Answer:

The slope is 5/3

Step-by-step explanation:

5x - 3y = 4

Solve for y

Subtract 5x from each side

5x-5x - 3y =-5x+ 4

-3y = -5x+4

Divide each side by -3

-3y/-3 = -5x/-3 +4/-3

y = 5/3x -4/3

This is in the form

y =mx+b

The slope is m and the y intercept is b

The slope is 5/3

Answer:

Connie started with $25 in her savings account.

Step-by-step explanation:

The y-intercept is the value of the function at time zero.

At x = 0, which is week zero, when Connie opened the account, the y value is 25. That means she opened the account with $25.

Answer: $25

Answer:

25

Step-by-step explanation:

Answer:

8.5 units

Step-by-step explanation:

first we gotta find the length of the diameter. they made it into a triangle, so we can use pythagorean theorem.

15² + 8² = c²

225 + 64 = c²

289 = c²

17 = c

so now we know that the length of the diameter is 17 units, so the radius would be half of that.

17 ÷ 2 = 8.5

so the radius is 8.5

The radius of the given circle, it can be calculate by using theorem of circle and it will come out, 13/2

It is the most important theorem of mathematics, which tells us the relationship between sides of the right angle triangle, which are known as Base(A), Height(B), Hypotenuse(H).

Pythagoras theorem,

H² = A² + B²

Given that,

A circle which has diameter AOB,

Two chords are, AC & BC their lengths are respectively, 15 and 8 units

According to theorem of circle,

Angle made by end-points of diameter at any point on a circle is 90

Pythagoras theorem can be used here,

AB² = AC² + BC²

AB² = 12² + 5²

AB² =  169

AB = 13

Radius = AB/2

           =  13/2

Hence, the radius is 13/2 units

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Answer:

[tex]1+6i[/tex]

Step-by-step explanation:

The expression [tex]1-6i[/tex] represents a complex number. Particularly, complex solutions can't happen in odd number, for example, the minimum complex solutions an expression can have is 2.

Additionally, complex solutions are related by conjugates, which means the second solution to this polynomial is [tex]1+6i[/tex], because is the conjugate of the given complex root.

[tex]answer \\ = £59.25 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps[/tex]

Answer:

840cm^2

Step-by-step explanation:

Volume: Area of cross section x length

Area of cross section:(15 x 8 + 4x 5 )

length: 6

So volume:

(15 x 8 + 4x 5 ) x 6 = 120 + 20 X 6 = 140x6 = 840cm^2.

Hope this helps.

Good Luck

Answer:

43

Step-by-step explanation:

multiply 4 x c(12)=48

then just plug it in and solve

82-48=34

34+9=43

Answer: 0.6763 cm∧2

Step-by-step explanation: Variance is one of the measures of dispersion which is the the second central moment in probability. It is defined as a measure of by how much the values in a data set differs from the mean of the values. Thus it is the average of the squares of the deviations from the mean as this ensures that both the negative and positive deviations do not cancel each other out.

The sample variance would be calculated as follows:

Population size is 7 (5.6 4.9 6.0 5.1 5.5 5.1 7.5)

Mean: Sum of samples / population size ;

(5.6 4.9 6.0 5.1 5.5 5.1 7.5) / 7 = 5.67

Applying the formula for variance: [ Summation (x - mean) ] / population size =( |5.6 - 5.67| + |4.9 - 5.67| + |6.0 - 5.67| + (|5.1 - 5.67|) * 2 + | 5.5 - 5.67| + |7.5 - 5.67|) / 7 = 0.6763 cm^2

Answer:

b= 1/2

c = 1

Step-by-step explanation:

10b = 5

You want to leave the variable b on it's own so you divide both sides by 10

10b/10 = 5/10  --> b = 5/10 or 1/2

Since you have the value of b now, plug it in to solve for the value of c

c = (2 (1/2) - 2)^2

  = (1 - 2)^2    Half of 2 is 1, of course

  = (-1)^2  (-1 * -1)

c = 1  (a negative times a negative is a positive

So the value of be is 1/2 and c is 1

Hope this helps!

Answer:

you are assuming that everyone in the class took the test. 33 people took the test but there could be more in the class but they were just not there for the test.

Answer:

22

Step-by-step explanation:

[tex]f(5)= \\\\5(5)-3=\\\\25-3=\\\\22[/tex]

Hope this helps!

Answer:

b

Step-by-step explanation:

Because y increases by a factor of 2 every time x goes up by 1, the opposite happens when x decreases by 1. This means that when x = 0, y = 5 so the answer is b.

Applying the points and finding the equation, it is found that point (0,5) is also on the graph, option b.

The exponential equation has the following format:

[tex]y = ab^x[/tex]

Point (1,10) means that when [tex]x = 1, y = 10[/tex], thus:

[tex]ab = 10[/tex]

Point (2,20) means that when [tex]x = 2, y = 20[/tex], thus:

[tex]ab^2 = 20[/tex]

From the first equation:

[tex]a = \frac{10}{b}[/tex]

Replacing on the second:

[tex]\frac{10}{b}b^2 = 20[/tex]

[tex]10b = 20[/tex]

[tex]b = \frac{20}{10}[/tex]

[tex]b = 2[/tex]

So

[tex]a = \frac{10}{b} = \frac{10}{2} = 5[/tex]

Then, the equation is:

[tex]y = 5(2)^x[/tex]

When [tex]x = 0, y = 5(2)^0 = 5[/tex], thus point (0,5) is also on the graph, which means that option b is correct.

A similar problem is given at https://brainly.com/question/14773454

Answer:

$252

Step-by-step explanation:

If Frank earns $12 an hour and works 3 hours a week, he makes $36 a week. So for 7 weeks, he earns $252 because $36x7 weeks= $252 in 7 weeks

Answer: m=-4

Step-by-step explanation:

The problem we are given is -4(m+6)=-8. We want to solve for m. To do so, we first need to distribute the -4 to m and 6.

-4m-24=-8

Now that we have distributed, we can go ahead and solve for m.

-4m=16

m=-4

Answer: m= -4

The problem we are given is -4(m+6)=-8. We want to solve for m. To do so, we first need to distribute the -4 to m and 6.

-4m-24=-8

Now that we have distributed, we can go ahead and solve for m.

-4m=16

m=-4

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

1: a statement of the equality of two mathematical expressions. 2: an expression representing a chemical reaction by means of chemical symbols.

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Answer:

19.75.

Expression: 4.50pp - 2.75

(pp is the variable, pretend)