30 points, Please help with trig

Answer:

Kristen would be 7.5 yo and Nicole would be 24.5 years old

Step-by-step explanation:

let x= kristen's age

3x+2= nicole's age

(3x+2)+x=32

4x+2=32

4x=30

x=7.5

3(7.5)+2= 24.5

Answer:

2x - 3y = -2 AND 4x + y = 24

Step-by-step explanation:

Simply plug in the coordinates into each answer choice, evaluate them, and you will have your answer.

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

Final answer:

To solve the equation ax - y = bx for x, add y to both sides, combine x terms, factor x out, and divide by (a - b) resulting in the solution x = y / (a - b).

Explanation:

To solve the given equation ax - y = bx for x, we aim to isolate x on one side of the equation:

First, we add y to both sides of the equation: ax = bx + y.

Next, we group the x terms together: ax - bx = y.

Then, we factor out x: x(a - b) = y.

Finally, we divide both sides by (a - b) to solve for x: x = y / (a - b).

So, the solution is x = y / (a - b).

Answer:

p=0.125

Step-by-step explanation:

2p+6p=1

Add like terms

8p=1

Divide both sides by 8 to get p by itself

8p/8=1/8

p=0.125

Answer:

D

Step-by-step explanation:

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Find the height of a rectangular prism if the surface area is 868, the width is 7 and the length is 31.

A.) 434

B.) 2.85

C.) 76

D.) 5.7

[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}[/tex]

[tex]\huge\colorbox{pink}{\color{black}{\boxed{D.) 5.7}}}[/tex]

[tex]\large\purple{ChaEunWoo2009}[/tex]

#CarryOnLearning

Answer:

At 11:30 am they will arrive at their starting point together

Step-by-step explanation:

we know that

One of them completes one lap in 6 minutes

The second one in 9 minutes

The third one in 15 minutes

step 1

Find the least common multiple (LCM)

6=2*3

9=3²

15=3*5

so

LCM=(3²)*(2)*(5)=90 minutes

step 2

Find the number of laps of each jogger for the LCM

jogger 1

90/6=15 laps

jogger 2

90/9=10 laps

jogger 3

90/15=6 laps

If they start at 10:00 am

then

10:00 am + 90 minutes=11:30 am

Answer:

Simplify 4y + 7x = 2t and there you go that's your answer☺

Step-by-step explanation:

Bucket = y

Jars = x

Tubs = t

y + 5x = t

3y + 2x = t

Answer:

Number of jars in one tub is:

13

Step-by-step explanation:

Let b denote the buckets, j denotes the jars and t denotes the tubs

One bucket + 5 jars equal one tub

b+5j=t   ----------------(1)

Three buckets plus two jars equal two tubs

3b+2j=2t   ------------------(2)

equation (1)×3- equation (2)

3(b+5j)-(3b+2j)= 3t-2t

3b+15j-3b-2j= t

13j= t

Hence, Number of jars in one tub is:

13

Answer:

Step-by-step explanation:

the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)

in this case, the zeroes are 3 and 6

Answer:

A. x = 3 and x = 6

Step-by-step explanation:

Zeros occur when the function crosses the x - axis. In this case, the quadratic function crosses the function when x = 3 and x = 6.

ANSWER

a. 16

b. 1

c. 64

d. 64

EXPLANATION

We want to simplify the following exponential expressions

a.

[tex] {2}^{4} [/tex]

This implies that

[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]

[tex] {2}^{4} = 16[/tex]

b. Any non-zero number exponent zero is 1.

This implies that,

[tex] {3}^{0} = 1[/tex]

c. The given exponentiial expression is,

[tex] {4}^{6} \times {4}^{ - 3} [/tex]

The bases are the same so we add the exponents.

[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]

This simplifies to,

[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]

[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]

d. We want to simplify:

[tex] { ({2}^{3}) }^{2} [/tex]

This is the same as

[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]

We add the exponents now to get:

[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]

To find the value of Lucy's house at the start of 2017, calculate a 5% increase each year from the initial £200,000 value in 2014. The compound value over the three years results in a house value of £231,525 at the start of 2017.

To calculate the value of Lucy's house at the start of 2017, we need to apply a 5% annual increase to the initial value of the house for three consecutive years (2014 to 2017).

Find the increase for the first year:

Initial value for 2014: £200,000

5% increase: £200,000 * 0.05 = £10,000

Value at the start of 2015: £200,000 + £10,000 = £210,000

Calculate the increase for the second year:

Value at the start of 2015: £210,000

5% increase: £210,000 * 0.05 = £10,500

Value at the start of 2016: £210,000 + £10,500 = £220,500

Calculate the increase for the third year:

Value at the start of 2016: £220,500

5% increase: £220,500 * 0.05 = £11,025

Value at the start of 2017: £220,500 + £11,025 = £231,525

Therefore, the value of Lucy's house at the start of 2017 would be £231,525.

11 is the base, meaning that it is the number being multiplied

3 is the exponent, meaning it tells you how many times you must multiply the base together

For this question we must multiply 11 together 3 times:

11*11*11 = 1331

Hope this helped!

Answer:

x = -3 , y = 2

Step-by-step explanation:

Solve the following system:

{y - 2 x = 8 | (equation 1)

{-3 x - y = 7 | (equation 2)

Swap equation 1 with equation 2:

{-(3 x) - y = 7 | (equation 1)

{-(2 x) + y = 8 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{-(3 x) - y = 7 | (equation 1)

{0 x+(5 y)/3 = 10/3 | (equation 2)

Multiply equation 2 by 3/5:

{-(3 x) - y = 7 | (equation 1)

{0 x+y = 2 | (equation 2)

Add equation 2 to equation 1:

{-(3 x)+0 y = 9 | (equation 1)

{0 x+y = 2 | (equation 2)

Divide equation 1 by -3:

{x+0 y = -3 | (equation 1)

{0 x+y = 2 | (equation 2)

Collect results:

Answer:  {x = -3 , y = 2

The solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2). The correct answer is option A.

Let's use the elimination method:

-2x + y = 8

-3x - y = 7

By adding the two equations together, we can eliminate the y variable:

(-2x + y) + (-3x - y) = 8 + 7

-2x - 3x + y - y = 15

-5x = 15

Dividing both sides by -5, we get:

x = -3

Now, substitute this value of x back into one of the original equations. Let's use -2x + y = 8:

-2(-3) + y = 8

6 + y = 8

y = 8 - 6

y = 2

Therefore, the solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2).

Therefore, the correct answer is option A.

Learn more about the linear equations here:

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The complete question is as follows:

The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations?

A. (–3, 2)

B. (–2, 3)

C. (2, –3)

D. (3, 2)

so, the cost will increase 2.8% per annum... so that simply means is a compound interest rate, so let's use the compound interest formula for this one.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$33741\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=\textit{years after 2015}\dotfill &t \end{cases} \\\\\\ A=33741\left(1+\frac{0.028}{1}\right)^{1\cdot t}\implies b(x)=33741(1.028)^x[/tex]

The complete expression for the compounding tuition fee function is [tex]b(x) = 33741(1.028) {}^{x} [/tex]

Using the compound interest relation :

[tex] b = P(1 + \frac{r}{n} ) {}^{nx} [/tex]

Where ;

The function b(x) can be written as :

[tex]b(x) = 33741(1 + \frac{0.028}{1} ) {}^{x} [/tex]

Therefore, the expression for the function b(x) is :

[tex]b(x) = 33741(1.028) {}^{x} [/tex]

Learn more : https://brainly.com/question/4290795

Answer:

2 2/5

Step-by-step explanation:

-1 3/5 ÷ -2/3

Change the mixed number to an improper fraction

-1 3/5 =  - (5*1 +3)/5 = -8/5

-8/5÷-2/3

Copy dot flip

-8/5 * -3/2

24/10

Divide top and bottom by 2

12/5

Change to a mixed number

12/5 = 2 2/5

Answer:

The point was reflected over the y-axis.

The point was translated left 6 units

Step-by-step explanation:

step 1

we know that

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite

In this problem

If you apply a reflection across the y-axis

(x.y)------> (-x,y)

(3,-2) ------> (-3,-2)

step 2

If you apply a translation to the left 6 units

The rule of the translation is equal to

(x,y)------> (x-6,y)

(3,-2) ------> (3-6,-2) ----> (-3,-2)

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

The area under the curve y = x^2 + 4 on the interval [-3,2] can be found using definite integration. The definite integral of a function gives us the net area between the function and the x-axis across the specified interval. To compute the area, we set up the integral from -3 to 2 of the function x^2 + 4.

To solve this, we integrate the function with respect to x:

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

Answer:

The answer B

Step-by-step explanation:

Answer:

The Average rate of change (the slope) is -4/3

Step-by-step explanation:

Find two Exact point like point A (-1,4) and point B (2,0)

Then count how many spaces does point A have to move left to right and down to get to point B.

since it moves down the number will be negative.

You will have to go 3 spaces to the right and 4 spaces down.

therefore giving you a slope of -4/3

To find the average rate of change for a given function, evaluate the function at the two given points and use the formula (f(2) - f(-1)) / (2 - (-1)).

To find the average rate of change for a given function, we need to calculate the difference in the values of the function between the two given points, and then divide that difference by the difference in the x-coordinates of the points. In this case, we are given x=-1 and x=2.

Let's evaluate the function at these two points:

f(-1) = ?, f(2) = ?

Once we have the values, we can calculate the average rate of change using the formula:

Average Rate of Change = (f(2) - f(-1)) / (2 - (-1))

Substitute the values and calculate to find the answer.

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Answer:

-13 < 16

Step-by-step explanation:

(4 is x, -5 is y)

-5 - 8 < 4(4)

-13 < 16

It is true and is a solution

Answer:

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Step-by-step explanation:

Step 1: Plug x and y into the inequality

-5 - 8 < -4(4)

Step 2: Simplify the inequality

-13 < -16

Step 3: Interpret and conclude

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Answer:

D. 33

Step-by-step explanation:

√(x-8) + 2 = 7

subtract 2 from both sides

√(x-8)  = 5

square both sides

(√(x-8))²  = 5²

x-8 = 25

add 8 to both sides

x = 33

ANSWER

D. 33

EXPLANATION

The given radical equation is

[tex] \sqrt{x - 8} + 2 = 7[/tex]

Group similar terms,

[tex]\sqrt{x - 8} = 7 - 2[/tex]

[tex]\sqrt{x - 8} = 5[/tex]

Square both sides:

[tex] {(\sqrt{x - 8})}^{2} = {5}^{2} [/tex]

Simplify

[tex]x - 8 = 25[/tex]

Solve for x

[tex]x = 25 + 8 = 3[/tex]

Answer:

12x^2+3x+6 and  -7x^2-4x-2 -> 5x^2-x+4

2x^2-x and -x-2x^2-2 -> -2x-2

x^3+x^2+2 and x^2-2-x^3 -> 2x^2

x^2+x and x^2+8x-2 -> 2x^2+9x-2

hope this helps :)

Answer:

180 -angle BCD

Step-by-step explanation:

if you've found angle BCD you should be able to find angle DCE as angles on a straight line equal 180°

Answer:

You had it correctly chosen, (9, infinity)

Step-by-step explanation:

Good job =)

ANSWER

[9,∞)

EXPLANATION

The given radical function is ;

[tex]f(x) = \sqrt{x - 9} [/tex]

This function is defined if and only if the expression under the radical sign is greater than or equal to zero.

[tex]x - 9 \geqslant 0[/tex]

[tex]x \geqslant 9[/tex]

Or

In interval notation, we have

[9,∞)

Answer:

Step-by-step explanation:

Add the square of half the x-coefficient to both sides.

 x² -12x +(-6)² = 61 +(-6)²

Answer:

x² - 12x + 36 = 97

Step-by-step explanation:

Given

x² - 12x = 61

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 6)x + (- 6)² = 61 + (- 6)², so

x² - 12x + 36 = 61 + 36

x² - 12x + 36 = 97

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5, hence

sum = 180° × 3 = 540°

Answer:

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Step-by-step explanation:

we know that

the equation of a circle into center radius form is equal to

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( 3,-2)

radius r=3 units

substitute

[tex](x-3)^{2} +(y+2)^{2}=3^{2}[/tex]

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Answer: A on edg

Step-by-step explanation:

Answer:

[tex]r=16\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the silo is equal to the volume of a cylinder plus the volume of a hemisphere

so

[tex]V=\pi r^{2}h+\frac{4}{6}\pi r^{3}[/tex]

In this problem we have

[tex]V=35,500\pi\ ft^{3}[/tex]

[tex]h=4D=8r[/tex] ----> 4 times the diameter is equal to 8 times the radius

substitute in the formula and solve for r

[tex]35,500\pi=\pi r^{2}(8r)+\frac{4}{6}\pi r^{3}[/tex]

Simplify pi

[tex]35,500=8r^{3}+\frac{4}{6}r^{3}[/tex]

[tex]35,500=r^{3}[8+\frac{4}{6}][/tex]

[tex]35,500=r^{3}[\frac{52}{6}][/tex]

[tex]r^{3}=35,500/[\frac{52}{6}][/tex]

[tex]r=16\ ft[/tex]

Answer:

c for sure

Step-by-step explanation:

(I got the question correct on my assignment)

The correct symbol to fill in the blank is: c. > (greater than)

Therefore, HJ < HG is the relationship between the angles HJ and HG based on the given angle measures.

To determine the relationship between the angles HJ and HG based on the given information, which states that angle H equals 80° and angle J equals 45°, we can utilize the properties of angles in a triangle.

Considering the angles in a triangle, the sum of the interior angles equals 180°. Therefore, if we have the measures of angles H and J in triangle HJG, we can find the measure of angle HG.

Given:

Angle H = 80°

Angle J = 45°

Let's calculate angle HG:

In a triangle, the sum of all angles is 180°.

So, angle HG = 180° - (angle H + angle J)

= 180° - (80° + 45°)

= 180° - 125°

= 55°

Therefore, angle HG measures 55°.

Now, to determine the relationship between HJ and HG:

Angle HJ is opposite angle HG within triangle HJG, and since angle H is greater than angle J, which implies that angle HG is greater than angle HJ.

Hence, the correct symbol to fill in the blank is:

c. > (greater than)

Therefore, HJ < HG is the relationship between the angles HJ and HG based on the given angle measures.

Complete Question:

IfH = 80° and J = 45°, then HJ ___ HG

Choose the correct symbol to put in the blank.

a.<

b.=

c.>

Answer:

Option A. [tex]10\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of the rectangle is equal to

A=LW

where

L is the length of rectangle

W is the width of rectangle

we have

[tex]A(-3,1),B(-2,-1),C(2,1),D(1,3)[/tex]

Plot the vertices

see the attached figure

L=AD=BC

W=AB=DC

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AD

[tex]A(-3,1),D(1,3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(3-1)^{2}+(1+3)^{2}}[/tex]

[tex]AD=\sqrt{(2)^{2}+(4)^{2}}[/tex]

[tex]AD=\sqrt{20}[/tex]

[tex]AD=2\sqrt{5}\ units[/tex]

Find the distance AB

[tex]A(-3,1),B(-2,-1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(-1-1)^{2}+(-2+3)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(1)^{2}}[/tex]

[tex]AB=\sqrt{5}[/tex]

[tex]AB=\sqrt{5}\ units[/tex]

Find the area

[tex]A=(2\sqrt{5})*(\sqrt{5})=10\ units^{2}[/tex]

Answer:

D. Even

Step-by-step explanation:

Given function is [tex]f\left(x\right)=-2x^4+3x^2[/tex].

Now we need to check if the given function is Even/Odd.

we know that if f(-x)=f(x) then function is called Even.

we know that if f(-x)=-f(x) then function is called Odd.

[tex]f\left(x\right)=-2x^4+3x^2[/tex]

[tex]f\left(-x\right)=-2(-x)^4+3(-x)^2[/tex]

[tex]f\left(-x\right)=-2x^4+3x^2[/tex]

[tex]f\left(-x\right)=f\left(x\right)[/tex]

Hence given function is an Even function.

So the correct choice is D. Even.