Determine the intercepts of the line.

5x-9=-8y-3

Answer:

8

Step-by-step explanation:

AD is half of AB

1/2 * 16 = 8

Answer:

8

Step-by-step explanation:

CD is an altitude. It is perpendicular to AB, and it splits AB in half. If AB=16, and CD splits AB in half, to find AD you would do this:

1/2AB

1/2·16=8

8 is your answer.

Yu can also see that AD and DB are congruent, so their values must be the same.

~Stay golden~:)

Answer:

the quotient is 4000 and the square is a perfect square

Step-by-step explanation:

120/0.03=4000

40 time 40 is 1600 so its perfectly square.

hope this helps

Answer:

The time after which the rocket hit the ground is 5 seconds

Step-by-step explanation:

Given as :

The distance of the cover by rocket at the height h = - 16 t² + 160 t

Let the time after which rocket hit the ground = T seconds

Now, When the rocket hits the ground, then at that time, the velocity of the rocket becomes zero.

I.e velocity = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Or, v = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Now, v = [tex]\frac{\partial h}{\partial t}[/tex]

Or, v = [tex]\frac{\partial (-16t^{2}+160t)}{\partial t}[/tex]

or, v = - 32 t + 160

Now, ∵ velocity of rocket after reaching the ground becomes zero

So, v = - 32 t + 160 = 0

Or, 32 t = 160

Or, t = [tex]\frac{160}{32}[/tex]

∴ t = 5 sec

So, The time after which the rocket hit the ground = 5 sec

Hence The time after which the rocket hit the ground is 5 seconds answer

To find when the rocket will hit the ground using the quadratic equation h = -16t² + 160t, solve for t when h=0; the rocket will hit the ground after 10 seconds.

To determine when the rocket will hit the ground given the equation h = -16t² + 160t, we need to find the value of t at which the height h is zero. The equation represents a quadratic equation, where t is the time in seconds after the rocket was fired, and h is the height of the rocket at any time t.

To solve for the time when the rocket hits the ground, we set h to zero and solve for t:

We discard the t = 0 since it represents the initial time at launch. Thus, the rocket will hit the ground after 10 seconds.

During this entire period, while the rocket is ascending and descending, it is important to consider the horizontal motion if analyzing its trajectory in more detail, but for this problem, we are only concerned with the vertical motion.

Answer:

7 x + y = 9

Step-by-step explanation:

Answer:− 1 x (small)2  y + 39 x(small)  2 + 30 x

Step-by-step explanation:

Answer:

0.5 891 7,800

Step-by-step explanation:

is because least always go first

To order from least to greatest, convert all measurements to grams: 7,800 mg becomes 7.8 g, and 0.5 kg becomes 500 g. The order is 7.8 g, 500 g, and 891 g.

To order the weights 891 g, 7,800 mg, and 0.5 kg from least to greatest, we first convert them all to the same unit. Given that there are 1,000 mg in a gram (g) and 1,000 g in a kilogram (kg), we can convert as follows:

Now that we have all the weights in grams, we can easily compare them:

Ordering these from least to greatest, we get: 7.8 g < 500 g < 891 g.

Answer:

For [tex]\left | x \right |[/tex] we will have positive values only.

[tex]\left | -2.7 |\right =2.7[/tex]

[tex]\left | -9 |\right =9[/tex]

Rest are positive so will give positive values out of the modulus function.

Step-by-step explanation:

The absolute value of any number is its positive value only.

As for example [tex](-2.7)[/tex] and [tex](2.7)[/tex] both are having equal distance from [tex]0[/tex] in a number line, one on the left other on the right side of the number line but are equidistant from [tex]0[/tex].

So absolute value of a number is its distance on number line from reference point [tex]0[/tex].

One by one we will work with all of our question.

[tex]\left | 10 |\right =10[/tex]

[tex]\left | 0.3 |\right =0.3[/tex]

[tex]\left | 0 |\right =0[/tex]

[tex]\left | -2.7 |\right =2.7[/tex]

[tex]\left | -9 |\right =9[/tex]

So we have to take the positive number out of the modulus function that is also called absolute value.

Answer:

The Area of rectangle A is  576 feet²  .

Step-by-step explanation:

Given as :

The width of rectangle A = 16 feet

The Length of rectangle A = 8 feet + The length of rectangle B

The width of rectangle B = 14 feet

Let The length of rectangle B = L feet

So, The Length of rectangle A = 8 feet + L feet

The perimeter of rectangle A + The perimeter of rectangle B = 156 feet

So, 2 × ( Length A + width A ) +  2 × ( Length B + width B ) = 156 feet

Or,  2 × ( 8 + L + 16 ) +  2 × ( L + 14 ) = 156 feet

Or,  2 ×( 24 + L ) +  2 × ( L + 14 ) = 156 feet

Or, 48 + 2 L + 2 L + 28 = 156

Or, 76 L + 4 L = 156

So, 4 L = 156 - 76

Or, 4 L = 80

∴  L = [tex]\frac{80}{4}[/tex] = 20 feet

So , The Length of rectangle A = 8 feet + 28 feet = 36 feet

And The width of rectangle A = 16 feet

So, Area of rectangle A = Length of rectangle A × width of rectangle A

I.e  Area of rectangle A = 36 × 16 = 576 feet²

Hence The Area of rectangle A is  576 feet²  . Answer

Answer: 292.50 dollars

Work Shown:

P = 650 is the the principal.

r = 0.09 is the interest rate in decimal form.

t = 5 is the number of years.

i = P*r*t

i = 650*0.09*5

i = 292.50 is the simple interest.

Given values:

Principle,

Rate,

Time,

As we know,

→ [tex]i = R\times r\times t[/tex]

By substituting the values, we get

      [tex]= 650\times 0.09\times 5[/tex]

      [tex]= 292.50[/tex]

Thus the response above is right.

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Answer:

3:31 PM

Step-by-step explanation:

When the planes arrives in San Francisco, the time is 4:91 or 5:31 PM(central time/yellow). From Central time period to pacific time period, the time decreases by 2 hours. 5:31 - 2 hours is 3:31. The time is still PM. Answer is 3:31 PM.

Answer:

3:31pm

Step-by-step explanation:

Because each 60mins=1hr

51+40=91 which equals an hour and thirty 1 minutes plus an hour and 40 minutes which equals 3:31

Hope I'm right good luck!!1

Answer:

$215.94

Step-by-step explanation:

You do 20% × $179.95 to get $35.99

Since the 20% is being added to your bill, you add it to your base price

$179.95 + $35.99 = $215.94

425 g for the 15 ounce box of cereal?

Answer:

$13.20

Step-by-step explanation:

so add the prices up 1.25+0.40 should be

$1.65 now multiply it by the 8 postcards he will send

so 1.65•8= $13.20

Answer:

Their mass at the start was 400 kg.

Step-by-step explanation:

Given:

The tyres on a car during a grand prix race are reduced in mass by 3%. Their mass is 388 kg at the end of the race.

Now, to find the mass at the start.

Let the mass at the start be [tex]x[/tex].

According to question:

[tex]x - 3 \%ofx= 388[/tex]

⇒[tex]x-\frac{3}{100}\times x = 388[/tex]

⇒[tex]x-0.03x =388[/tex]

⇒[tex]0.97x=388[/tex]

Dividing both sides by 0.97 we get:

⇒[tex]x=400[/tex]

Therefore, their mass at the start was 400 kg.

To find the original mass of the tyres before the 3% decrease,  we make a simple percentage calculation. By setting up the equation 97/100 * x = 388, we find that the original mass of the tyres was 400 kg.

The question posted is a mathematics problem related to understanding percentages and its application to real-life situations such as a Grand Prix race.

Given that the tyres at the end of the race have a mass of 388 kg, which is 97% of their original mass (since they lost 3%), we can find their original mass by setting up a simple percentage equation. We denote the original mass as 'x' and set up the equation: 97/100 * x = 388. To solve for 'x', we divide both sides of the equation by 97/100, which is equivalent to multiplying by its reciprocal, 100/97.

The solution to the problem is then calculated as following: x = 388 * (100/97) = 400 kg.

Hence, the original mass of the tyres was 400 kg.

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Answer:

35

Step-by-step explanation:

Answer:

[tex]\large\boxed{W=\dfrac{A}{L}}[/tex]

Step-by-step explanation:

[tex]A=LW\qquad\text{divide both sides by}\ L\neq0\\\\\dfrac{A}{L}=\dfrac{LW}{L}\\\\\dfrac{A}{L}=W[/tex]

Answer:

x ≤ 435

Step-by-step explanation:

Given is the following condition.

The sum of a number and 15 is less than and equal to 450.

So, if the number is x, then we have  

x + 15 ≤ 450

⇒ x + 15 - 15 ≤ 450 - 15

⇒ x ≤ 435

Therefore, the solutions of the number are either 435 or less than 435 up to negative infinity. ( Answer )

Answer:

f(3) = g(3)

Step-by-step explanation:

we know that

When solve a system of linear equations by graphing, the solution of the system is the intersection point both lines

The intersection point is common point for bot lines

In this problem

we have the system of equations

f(x)

g(x)

The intersection point is (3,6)

That means that the solution for the system is the point (3,6)

so

For x=3

The value of f(3)=6 and the value of g(3)=3

therefore

f(3)=g(3)

Verify the statements

Find the equation of the blue line f(x)

(0,-3) and (1,0)

the slope is

[tex]m=(0+3)/(1-0)=3[/tex]

The equation  in slope intercept form is equal to

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

Find the equation of the red line g(x)

(-3,0) and (0,3)

the slope is

[tex]m=(3-0)/(0+3)=1[/tex]

The equation  in slope intercept form is equal to

[tex]g(x)=x+3[/tex]

case 1) f(6) = g(3)

The statement is false

Because

For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]

For x=3 ----> [tex]g(3)=3+3=6[/tex]

therefore

[tex]f(6) \neq g(3)[/tex]

case 2) f(3) = g(3)

The statement is true

Because

For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]

For x=3 ----> [tex]g(3)=3+3=6[/tex]

therefore

[tex]f(3)=g(3)[/tex]

case 3) f(3) = g(6)

The statement is false

Because

For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]

For x=6 ----> [tex]g(6)=6+3=9[/tex]

therefore

[tex]f(3) \neq g(6)[/tex]

case 4) f(6) = g(6)

The statement is false

Because

For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]

For x=6 ----> [tex]g(6)=6+3=9[/tex]

therefore

[tex]f(6) \neq g(6)[/tex]

Answer:

f(3)=g(3)

Step-by-step explanation:

Edge 2021

Answer:

17/4

Step-by-step explanation:

2 5/6=17/6

4/6=2/3

------------------

(17/6)/(2/3)=(17/6)(3/2)=51/12=17/4

Number line is the line in which the numbers are marked at the intervals to the show the inequality. The value of the x, is 2 which is shown on the number line by attached image below.

The equations given in the problem are,

[tex] 5 x + 4 = 14[/tex]

Number line is the line in which the numbers are marked at the intervals to the show the inequality.

Here in the problem the given equation is,

[tex] 5 x + 4 = 14[/tex]

Solve it for the x,

[tex]\begin{aligned}\\ 5 x &= 14-4\\ 5x&=10\\ x&=\dfrac{10}{5} \\ x&=2\\ \end[/tex]

The value of the x is 2. It can be shown on the number line graph by making a circle on the number 2.

As the inequality is shown with the equal sign in the given equation. Therefore the direction would be nigher side. The graph for the given equation number line shown in the attached image.

Hence the value of the x, is 2 which is shown on the number line by attached image below.

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Final answer:

To solve the equation 5x + 4 = 14, subtract 4 from both sides, then divide by 5. This gives x = 2, which can be checked by substitution back into the equation and verifying it holds true.

Explanation:

To solve the equation 5x + 4 = 14, we need to isolate the variable x. First, we subtract 4 from both sides of the equation to get 5x = 10. Next, we divide both sides of the equation by 5 to find the value of x:

5x ÷ 5 = 10 ÷ 5

x = 2

This means that the value of x that satisfies the equation 5x + 4 = 14 is 2. We can check our answer by substituting 2 back into the original equation to see if it makes a true statement:

5(2) + 4 = 10 + 4 = 14

Since the left side of the equation equals the right side, x = 2 is indeed the solution.

Answer:

I am going to assume you mean the relationship between x and y.

If the y-intercept is 0, that means the point is on the origin.

So x and y are equal to each other. they are both zero

Answer: The y-intercept represents what is the value of y when x=0.

Paying an extra $100 each month on a $60,000 loan with an 8% APR over 25 years will reduce the loan term and total interest paid. To calculate the effect, compute the total cost of the loan with and without the extra payments and subtract these two sums.

The subject at hand pertains to understanding the impact of additional payments on a loan, which falls under the domain of financial mathematics. Let's dissect the impact of paying an extra $100 per month on a $60,000 loan with an 8% annual interest rate over 25 years.

Firstly, we need to calculate the monthly payment for a 25-year loan of $60,000 at 8% interest. This can be calculated by using a loan calculator or the loan payment formula. Then, calculate the total cost of the loan by multiplying this monthly payment by the number of months in the loan term (25 years x 12 months).

You then do a similar calculation, but this time add an extra $100 to the monthly payment. The extra repayment will reduce the loan term and decrease the total interest paid. To see the effect, compare the total cost of the loan with and without the extra $100.

Therefore, the difference between these two sums will give you the saved amount due to the additional $100 monthly payment. This saving is the effect of making additional payments on the loan.

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Making additional monthly payments can shorten the loan term and save money on interest payments.

To calculate the effect of making additional monthly payments on the cost of the loan, we can compare the total interest paid and the duration of the loan with and without the additional payments. Without any additional payments, the monthly payment for a $60,000 loan with an 8% APR and a 25-year term would be $459.18. With an additional $100 each month, the monthly payment would increase to $559.18.

By making the additional $100 payments, the loan would be paid off faster, reducing the term from 25 years to approximately 17 years and saving the borrower 8 years of monthly payments. Additionally, the total interest paid over the course of the loan would also be significantly reduced compared to just paying the required monthly payments.

In summary, making extra monthly payments of $100 can shorten the loan term and save the borrower money on interest payments.

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Answer: 1/10

Step-by-step explanation:

There is  1 yellow marble out of the 10 marbles

Answer:

Step-by-step explanation:

1/9

8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2

Solution:

Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'

Need to find the ratio of a:b

As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.  

For sake of simplicity, let volume of 1 sphere of radius a cm is represented by [tex]V_a[/tex] and volume of 1 sphere of radius b cm is represented by [tex]V_b[/tex]

So volume of 8 solid iron sphere with radius 'a cm' = volume of  1 solid iron sphere with radius 'b cm'

[tex]=>8 \times} \mathrm{V}_{\mathrm{a}}=\mathrm{V}_{\mathrm{b}}[/tex]

[tex]\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{b}}}=\frac{1}{8}[/tex]  ---- eqn 1

[tex]\text {Let's calculate } {V}_{a} \text { and } V_{b}[/tex]

Formula for volume of sphere is as follows:

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

Where r is radius of the sphere

Substituting r = a cm in the formula of volume of sphere we get

[tex]V_{a}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi a^{3}[/tex]

Substituting r = b cm in the formula of volume of sphere we get

[tex]V_{b}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi b^{3}[/tex]

[tex]\text { Substituting value of } V_{a} \text { and } V_{b} \text { in equation }(1) \text { we get }[/tex]

[tex]\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}[/tex]

[tex]\begin{array}{l}{=>\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}} \\\\ {=>\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{2}\right)^{3}} \\\\ {=>\frac{a}{b}=\frac{1}{2}}\end{array}[/tex]

a : b = 1 : 2

Hence the ratio of a:b is 1 : 2

Final answer:

The ratio of the radius 'a' of the original smaller spheres to the radius 'b' of the new larger sphere formed by melting the 8 smaller spheres together is 1:2, obtained by equating the volumes and simplifying.

Explanation:

The question pertains to using the concept of volumes of spheres in Mathematics to find the ratio of radii of the original smaller spheres to the new larger sphere formed by melting them together. Given that there are 8 solid iron spheres each with radius 'a cm', and they are melted to form one single sphere with radius 'b cm', we preserve the volume during the melting process.

We know that the volume of a sphere is calculated using the formula [tex]V=\frac{4}{3}\pi r^{3}[/tex]. When combining the volumes of the 8 smaller spheres into one large sphere, the volumes on both sides must be equal since no material is lost during melting. The equation to find the volume of the large sphere is [tex]V=8(\frac{4}{3}\pi a^{3}) = \frac{4}{3}\pi b^{3}[/tex].
Simplifying this equation, we obtain the cubic ratio of radii a³/b³ = 1/8. Taking the cube root of both sides, the simple ratio of the radii is a/b = ∛[1/8], which simplifies to a/b = 1/2. Therefore, the ratio of the radius of the smaller sphere to the radius of the larger sphere, a:b, is 1:2,

Answer: -1, 0, and 1

Step-by-step explanation: -1 is an integer and all integers are rational numbers so -1 is rational.

0 is also an integer and all integers are rational numbers. Therefore, 0 is considered a rational number.

1 is a natural number and all natural numbers are rational numbers. Therefore, 1 would be a rational number.

Answer:

Linear

Step-by-step explanation:

Because it has no exponents

If it has no exponents than its always linear

Answer:

Linear

Step-by-step explanation:

It is in Slope-Intercept Form [y = mx + b], and this formula is ALWAYS a linear function [NO EXPONENTS].

I am joyous to assist you anytime.

Answer:

Option 1. Lynn, only

Step-by-step explanation:

The correct question is

Listen Lynn, Jude, and Anne were given the function f(x)=-2x^2+32, and they were asked to find f(3). Lynn's answer was 14, Jude's answer was 4, and Anne's answer was (+/-)4. Who is correct?

1. Lynn, only

2. Jude, only

3. Anne, only

4. Both Lynn and Jude

we have

[tex]f(x)=-2x^{2} +32[/tex]

This is a vertical parabola open downward (leading coefficient is negative)

The vertex is a maximum

we know that

f(3) means, the value of f(x) when the value of x is equal to 3

so

For x=3

substitute in the quadratic equation and solve for f(x)

[tex]f(3)=-2(3^{2}) +32[/tex]

[tex]f(3)=-18 +32[/tex]

[tex]f(3)=14[/tex]

therefore

Lynn's answer is correct

To determine the value of the function f(x) = 2x + 32 at x=3, we substitute x with 3, and solve to obtain f(3) = 38. Therefore, all students' answers were incorrect.

In the function f(x) = 2x + 32, to find the value of f(3), you first need to substitute 'x' with 3. The equation it becomes f(3) = 2 * 3 + 32

By solving the equation, you obtain is f(3) = 6 + 32 which equals to f(3) = 38.

Thus, all the students, Lynn, Jude, and Anne, unfortunately provided incorrect answers.

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