If theta is an acute​ angle, solve the equation tangent theta equals four fifths
. Express your answer in​ degrees, rounded to one decimal place.

Answer:

Step-by-step explanation:

(x-3)*(x+3)

we begin by expanding and then simplifying

= (x²+3x-3x-9)

= x² - 9

Answer:

x² - 9

Step-by-step explanation:

hello :

(x - 3 ) (x + 3) = x²+3x-3x-9

(x - 3 ) (x + 3) = x² - 9

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2)  [tex]y=100x+300[/tex]

Part 3) [tex]\$12,300[/tex]

Part 4) [tex]\$2,700[/tex]

Part 5) Is a exponential growth function

Part 6) [tex]A=6,000(1.07)^{t}[/tex]

Part 7) [tex]\$11,802.91[/tex]

Part 8)  [tex]\$6,869.40[/tex]

Part 9) Is a exponential growth function

Part 10) [tex]A=5,000(e)^{0.10t}[/tex]    or  [tex]A=5,000(1.1052)^{t}[/tex]

Part 11)  [tex]\$13,591.41[/tex]

Part 12) [tex]\$6,107.01[/tex]

Part 13)  Natalie has the most money after 10 years

Part 14)  Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

[tex]m=\$100\ per\ month[/tex]

The y-intercept or initial value is

[tex]b=\$300[/tex]

so

[tex]y=100x+300[/tex]

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

[tex]10\ years=10(12)=120 months[/tex]

For x=120 months

substitute in the linear equation

[tex]y=100(120)+300=\$12,300[/tex]

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

so

[tex]2\ years=2(12)=24\ months[/tex]

For x=24 months

substitute in the linear equation

[tex]y=100(24)+300=\$2,700[/tex]

Part 5) What type of exponential model is Sally’s situation?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$6,000\\ r=7\%=0.07\\n=1[/tex]

substitute in the formula above

[tex]A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}[/tex]

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute  the value of t in the exponential growth function

[tex]A=6,000(1.07)^{10}=\$11,802.91[/tex] 

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute  the value of t in the exponential growth function

[tex]A=6,000(1.07)^{2}=\$6,869.40[/tex]

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex] 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]P=\$5,000\\r=10\%=0.10[/tex]

substitute in the formula above

[tex]A=5,000(e)^{0.10t}[/tex]

Applying property of exponents

[tex]A=5,000(1.1052)^{t}[/tex]

 therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

[tex]A=5,000(e)^{0.10t}[/tex]    or  [tex]A=5,000(1.1052)^{t}[/tex]

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

[tex]A=5,000(e)^{0.10*10}=\$13,591.41[/tex]

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

[tex]A=5,000(e)^{0.10*2}=\$6,107.01[/tex]

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

Answer:

[tex]-16x^2[/tex]

Step-by-step explanation:

[tex](2x)^2 * -4\\=4x^2*-4\\=-16x^2[/tex]

Answer:

0

Step-by-step explanation:

An exponent multiply's that number by that amount of the exponent.

EX : 2^3 where ^ represents exponent

You would write it out like :2*2*2=8

Your problem asks us to multiply the number 2 by itself twice, equaling 4

and 4 subtracted by 4 is zero .

Final answer:

Using an algebraic approach, we found out that if Barbara is 142 cm tall, which is 2 cm less than three times her birth height, then her height at birth was 48 cm.

Explanation:

The question asks us to determine Barbara's height at birth given that she is currently 142 cm tall and that this height is 2 cm less than three times her height at birth. To find her height at birth, we can construct and solve a simple algebraic equation based on this information.

Let h represent Barbara's height at birth. The problem states that:

142 cm = 3h - 2 cm

Adding 2 cm to both sides of the equation, we get:

144 cm = 3h

Dividing both sides of the equation by 3 so we can solve for h, gives us:

h = 144 cm / 3

h = 48 cm

Therefore, Barbara's height at birth was 48 cm.

Answer:

Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Step-by-step explanation:

Quotient is the required answer if 584 is divided by 17

584 will be the dividend and 17 is the divisor.

To calculate 584/17, 17 will go in 58 3times with 7 as remainder. This remainder 7 will combine with 4 to make 74, 17 will also go in 74 4times with remainder of 6.

The final answer by combining the number of times 17 goes in 584 which is 34 with final remainder of 6. This means that;

584/17 = 34 remainder 6 i.e 34R6

This shows that Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Answer:

The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of fliers the volunteers gave for a political campaign = 21/38

Remaining 612 were given out in another neighborhood

2. What is the total number of fliers they gave out?

x = Total of fliers

21x/38 = Fliers given out in the first neighborhood

612 = Fliers given out in the second neighborhood

Let's solve for x, this way:

x - 21x/38 = 612

38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)

17x = 23,256

x = 23,256/17

x = 1,368

The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.

Answer:No

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

u had 11 and u spent 7

7/11 <=== the fraction of money u spent is 7 out of 11

Answer:

He have 47 ducks and 7 cows.

Step-by-step explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.

Let the number of ducks be [tex]x.[/tex]

And the number of cows be [tex]y.[/tex]

So, total number of animals are:

[tex]x+y=54[/tex]

[tex]x=54-y[/tex]  ....( 1 )

As, the feet of cows are 4 and ducks are 2.

Now, the total number of feet are:

[tex]2(x)+4(y)=122[/tex]

[tex]2x+4y=122[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]2(54-y)+4y=122[/tex]

[tex]108-2y+4y=122[/tex]

[tex]108+2y=122[/tex]

Subtracting both sides by 108 we get:

[tex]2y=14[/tex]

Dividing both sides by 2 we get:

[tex]y=7.[/tex]

The number of cows = 7.

Now, to get the number of ducks we substitute the value of [tex]y[/tex] in equation (1):

[tex]x=54-y\\x=54-7\\x=47.[/tex]

The number of ducks = 47.

Therefore, he have 47 ducks and 7 cows.

Answer:

14

Step-by-step explanation:

The revenue earned is represented by t(x)=5x. Since the equation asks for the profit after four seasons you fill in 4 for x and get 20. r(x)=(1.5)x is how much it costs to pay their employees each season so you fill in 4 for x. Now you take revenue earned and subtract it by the cost to pay employees and you get the profit.

5x - 1.5x = Profit

5(4) - 1.5(4) = Profit

20 - 6 = Profit

14 = Profit

Answer:

15

Step-by-step explanation:

Answer:

C(g) = 2.19g ; 2.5

Step-by-step explanation:

Question 1

Since the cost is $2.19 per gallon. For every gallon, the cost will increase by $2.19. Hence, the cost per gallon C(g) is 2.19g.

Question 2

f(1.5) = 3(1.5) - 2

= 4.5 - 2

= 2.5

Answer:

1. C(g) = 2.98g

2. 2.5

Step-by-step explanation:

1. 1 gallon cost $2.98

Therefore y gallon will cost = y2.98 ie C(g) = 2.98g

2. F(x) = 3x — 2

F(1.5) = 3x1.5 — 2 = 4.5 — 2 = 2.5

Answer:5/8

Step-by-step explanation:

Answer:

The product of a non-zero rational number and an irrational number will always be an irrational number.

Step-by-step explanation:

Here's a proof by contradiction for this claim.

Consider an irrational number [tex]x[/tex]. Assume by contradiction that this claim isn't true. In other words, assume that there exist a non-zero rational number [tex]y[/tex] such that [tex]x \cdot y[/tex] is a rational number.

By the definition of rational numbers, a number is a rational number if and only if it can be written as the quotient of two integers.

Divide [tex]y[/tex] from both sides of the equation:

[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/y[/tex].

The left-hand side of this equation is now equal to [tex]x[/tex].

Since [tex]\displaystyle y = \frac{a}{b}[/tex]  by assumption, the [tex]y[/tex] on the right-hand side of this equation can be replaced with [tex]\displaystyle \frac{a}{b}[/tex]. Hence, the right-hand side of this equation would become

[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/\frac{a}{b} = \frac{c}{d}\cdot \left(\frac{b}{a}\right) = \frac{b \cdot c}{a \cdot d}[/tex].

Combine the two sides of the equation to obtain:

[tex]x = \displaystyle \frac{b \cdot c}{a \cdot d}[/tex].

Since [tex]b[/tex] and [tex]c[/tex] are both integers, their product [tex]b \cdot c[/tex] would also be an integer. Similarly, since [tex]a[/tex] and [tex]d[/tex] are both integers, their product [tex]a \cdot d[/tex] would also be an integer.

In other words, [tex]x[/tex] can now be represented as the quotient of two integers. By the definition of rational numbers,

Hence, the original assumption that this claim isn't true, is not true. That verifies the claim that the product of a non-zero rational number and an irrational number would be an irrational number.

answer: 28: 4

21: 3

70: 10

step-by-step explanation:

divide 28 by 4, and of course, do to the bottom what you do to the top. 4 divided by 4 is 1, and 28 divided by 4 is 7.

7: 4.

then, multiply by the number of smoothies.

for 3, it's 21: 3.

for 10, it's 70: 10.

Answer:

-.15

Step-by-step explanation:

you first do whats in the parantheses (3/4 - 1) which equals -.25, then multiply by 2 which gives you -.5, now add .35 and your total is -.15

Answer:

0.85

Step-by-step explanation:

2(3/4-1)+0.35

=(1.5-1)+0.35

=0.5+0.35

=0.85

Answer:

[tex]y=-1.5x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem we have

y=15/2 when x=-5

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the given values

[tex]k=\frac{(15/2)}{-5}=-1.5[/tex]

therefore

The linear equation that relates x and y is equal to

[tex]y=-1.5x[/tex]

Answer:

The age of Noelle's dad is 54 years and that of Noelle is 20 years.

Step-by-step explanation:

Let the age of Noelle's dad is x years and that of Noelle is (74 - x) years.

{Since, the sum of their ages is 74}

Now, given that the age of Noelle's dad is 6 less than 3 times Noelle's age.

So, 3(74 - x) - 6 = x

⇒ 4x = 222 - 6 = 216

⇒ x = 54

So, the age of Noelle's dad is 54 years and that of Noelle is (74 - 54) = 20 years. (Answer)

Answer:7

Step-by-step explanation:

Answer:

Technically, since it's an improper fraction, turning it into a whole number is not possible.

Step-by-step explanation:

21/4 as a decimal is 5.25

5.25 as a mixed number would be 5 1/4. Therefore, the closest 21/4 can get to a "whole number" is 5.

1) Turn everything into improper fractions: 10/3, 17/6, and 11/4

2) Find LCM of 3, 6, and 4: 12

3) Fix improper fractions to match the new denominator: 40/12, 34/12, and 33/12

4) Add them all up: 40/12+34/12+33/12=107/12=8 11/12

So your final answer is 8 11/12

Hope this helped and please mark as brainliest!

Answer:

Minimum value is 0

Maximum value is undefined.

Step-by-step explanation:

The given function is [tex]f(x)=7x^2[/tex]

This function is a parabola that has its vertex at the origin.

The coefficient of the quadratic term is 7, which is greater than zero.

This means that, the graph will open up.

The graph will therefore have a minimum value of y=0

The graph  of this function does not have a maximum value.

Answer:

here is the answer, out of all my experience i'm not too good on these word problems. You should check number two but if you agree than yay.

Step-by-step explanation:

Answer:

Step-by-step explanation:

D=rt

180miles = 45mph* times

180miles/45mph =time

Time = 4hours

2/1 frptrhgqhgr4tjtfix jxcfh8u5t8ofszYI7wyt439tfy7efgy5g

Final answer:

Bees can see 4 out of the 6 pure spectral colors, which simplifies to the fraction 2/3 after removing the 2 colors they cannot see, orange and red.

Explanation:

The question involves calculating a fraction, which is a basic mathematical concept. We are told there are 6 pure spectral colors: red, orange, yellow, green, blue, and violet. Bees cannot see orange or red, so we must find out what fraction of the 6 pure spectral colors bees can see. We subtract the 2 colors bees can't see (orange and red) from the total of 6, leaving us with 4 colors they can see which are yellow, green, blue, and violet.

To express this as a fraction, we take the number of colors bees can see (4) and place it over the total number of pure spectral colors (6). Therefore, the fraction of pure spectral colors that bees can see is 4/6. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Thus, the simplified fraction is 2/3.

Answer:

[tex]f(3)=-60[/tex]

Step-by-step explanation:

[tex]f(3)=5(3)^2-7(4(3)+3)\\\\f(3)=5(3)^2-7(12+3)\\\\f(3)=5(3)^2-7(15)\\\\f(3)=5\times 9-7\times 15\\\\f(3)=45-105\\\\f(3)=-60[/tex]

Answer:

The y-intercept

Answer:

b

Step-by-step explanation:

I am thinking it would be "b" because y=mx+b so not the multiple choice but whichever one says b

Answer: I guessed on the second one

Step-by-step explanation:

The problem falls under mathematics, more specifically algebra, using a system of two equations to solve for the timing of the cardio and weighted workouts. The equations can be formed from the provided data and can be solved using substitution or the elimination method.

This problem is a system of equations questions in mathematics, specifically in the subset of algebra. To be able to solve this, you need to create two equations from the data provided on the table and then solve for both cardio and weighted workout timings. For instance, if I did 2 cardio workouts and 3 weighted workouts in week 1 for a total of 150 minutes and 3 cardio workouts and 1 weighted workout in week 2 for a total of 160 minutes, you can construct these two equations:

2*cardio + 3*weighted = 150 (Equation for week 1)

3*cardio + weighted = 160 (Equation for week 2)

Next, you solve this system of equations either by substitution or elimination- whatever you're more comfortable with. The results will give you the duration of each cardio and weighted workout.

https://brainly.com/question/35467992

#SPJ11

B

Step-by-step explanation:

(1)Area of triangle= 1/2 x height (7cm) x base (8cm)

= 56/2

= 28

(2)Area of circle = (Pi)r^2

= (Pi)4cm^2

= 50.26548....

Since the circle is half divide the above by 2

= 25.132741.....

Round the answer to the nearest hundredth

= 25.13

(1) + (2)

28+25.13= 53.13

Hope this helps! :)

To write the given expression (4f-3+2g)-(-4g+2) in standard form, change the signs of the terms subtracted and combine like terms to simplify to 4f + 6g - 5.

To write the expression in standard form, you need to simplify the expression by combining like terms and handling the subtraction of negative numbers properly. Given the expression (4f-3+2g)-(-4g+2), you first remove the parenthesis while changing the signs of the terms inside the parenthesis being subtracted.

The expression -(-4g+2) will become +4g-2 once we apply the rule that subtracting a negative is the same as adding a positive, similarly to the example 2-(-6)=2+6=8.

Now the expression is simplified to 4f - 3 + 2g + 4g - 2. We combine like terms to get 4f + 6g - 5.

The standard form of the given expression is 4f + 6g - 5.

The expression (4f-3+2g)-(-4g+2) can be simplified using the distributive property and combining like terms.

First, distribute the negative sign to the terms inside the parentheses: (-1) * (-4g) = 4g and (-1) * 2 = -2.

The expression becomes (4f-3+2g) + (4g-2).

Next, combine like terms: 4g + 2g = 6g, and -3 - 2 = -5.

The final expression in standard form is 4f + 6g - 5.