equation
slope (m) =
y-intercept =_4

Answer:

Viewing window: [0, 1.4] × [-3, 12]

See the attachments from the TI-83 Plus graphing calculator.

1) f(t) = -16t² + 15t + 6.5

2) -16t² + 15t + 6.5 = 0

32t² - 30t - 13 = 0

t = (30 + √((-30)² - 4(32)(-13)))/(2(32))

= (30 + √2564)/64

= (30 + 2√641)/64

= (15 + √641)/32

= about 1.26 seconds

3) f'(t) = -32t + 15

-32t + 15 = 0

t = 15/32 seconds = about .47 seconds

f(15/32) = -16(15/32)² + 15(15/32) + 6.5

= about 10.02 feet

Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]

Part 2: It takes approximately 0.89 seconds for the basketball to hit the ground.

Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.

Part 1: The function that models the height of the basketball is given by:

[tex]\[ h(t) = -16t^2 + v_0 t + h_0 \][/tex]

Given:

- Initial velocity [tex](\( v_0 \))[/tex] = 15 ft/sec

- Initial height [tex](\( h_0 \))[/tex] = 6.5 feet

So, the function becomes:

[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]

Part 2: To find how long it takes for the basketball to hit the ground, we set [tex]\( h(t) = 0 \)[/tex] and solve for [tex]\( t \)[/tex]:

[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]

We can use the quadratic formula to solve for[tex]\( t \)[/tex]:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where [tex]\( a = -16 \), \( b = 15 \), and \( c = 6.5 \).[/tex]

Plugging in the values:

[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \]\[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \]\[ t = \frac{-15 \pm \sqrt{641}}{-32} \][/tex]

Using a calculator, we find:

[tex]\[ t \approx 0.89 \text{ seconds (rounded to the nearest hundredth)} \][/tex]

Part 3: To find when the basketball reaches its maximum height, we can use the formula for the x-coordinate of the vertex of a quadratic function:

[tex]\[ t_{\text{max}} = -\frac{b}{2a} \][/tex]

For our function [tex]\( h(t) = -16t^2 + 15t + 6.5 \), \( a = -16 \) and \( b = 15 \).[/tex]

[tex]\[ t_{\text{max}} = -\frac{15}{2(-16)} \]\[ t_{\text{max}} = \frac{15}{32} \]\[ t_{\text{max}} \approx 0.47 \text{ seconds (rounded to the nearest hundredth)} \][/tex]

Part 4: To find the maximum height of the basketball, we substitute the value of [tex]\( t_{\text{max}} \)[/tex] into the function [tex]\( h(t) \):[/tex]

[tex]\[ h_{\text{max}} = -16(0.47)^2 + 15(0.47) + 6.5 \]\[ h_{\text{max}} = -16(0.2209) + 7.05 + 6.5 \]\[ h_{\text{max}} = -3.5344 + 7.05 + 6.5 \]\[ h_{\text{max}} \approx 10.0156 \text{ feet (rounded to the nearest hundredth)} \][/tex]

The maximum height of the basketball is approximately 10.02 feet.

Solving the inequality [tex]2+s\geq 10\,\,,where\,\,s=7[/tex] we get [tex]9\geq 10\,\,(not\,\,true)[/tex]

We know that 9 is not greater than 10 so, the inequality doesn't hold.

Step-by-step explanation:

We need to solve:

[tex]2+s\geq 10\,\,,where\,\,s=7[/tex]

Solving the inequlaity:

[tex]2+s\geq 10[/tex]

Putting value of s i.e s=7 in the equation

[tex]2+7\geq 10\\9\geq 10[/tex]

Solving the inequality [tex]2+s\geq 10\,\,,where\,\,s=7[/tex] we get [tex]9\geq 10\,\,(not\,\,true)[/tex]

We know that 9 is not greater than 10 so, the inequality doesn't hold.

Keywords: Solving inequalities

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Answer:

Option B.

Step-by-step explanation:

Given information: ∠MHL=(3x+20), ∠KHN=(x+25), and ∠JHN=(x+20).

We need to find the measure of ∠JHN.

[tex]\angle MHL=\angle JHK[/tex]                         (Vertical opposite angles)

[tex]\angle MHL=\angle JHN+\angle KHN[/tex]

Substitute the given values.

[tex]3x+20=(x+20)+(x+25)[/tex]

[tex]3x+20=2x+45[/tex]

[tex]3x-2x=45-20[/tex]

[tex]x=25[/tex]

The value of x is 25. So, the measure of ∠JHN is

[tex]\angle JHN=x+20=25+20=45[/tex]

The measure of ∠JHN is 45°.

Therefore, the correct option is B.

Answer:

it's B

Step-by-step explanation:

Answer:

6.3 x 10°

Step-by-step explanation:

6.3 can be written as 6.3 x 1

recall that anything to the power of zero = 1

hence 10° = 1 substitute this back into the expression above to get:

6.3

= 6.3 x 1

= 6.3 x 10°

Answer:

Step-by-step explanation:

We are given two relations we can use to find "a" and "b":

  a = 3b

  a² + b² = 30²

Substituting for "a", we have ...

  (3b)² +b² = 900

  10b² = 900

  b² = 90

  b = √90 = 3√10 ≈ 9.5

Then "a" is ...

  a = 3b = 3(3√10) = 9√10 ≈ 28.5

The values of "a" and "b" are about 28.5 and 9.5, respectively.

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Solution:

Given roots of the polynomial are:

–3, –2, 1 and 5

If a is the root of the polynomial then the factor is (x –a).

So that, the factors of the given roots are:

(x –(–3)) = x + 3

(x –(–2)) = x + 2

(x – 1) = x – 1

(x – 5) = x –5

Polynomial = Product of the factors

                    = (x + 3)(x + 2)(x – 1)(x – 5)

Multiply first two factors.

                     [tex]=(x^2+2x+3x+6)(x-1)(x-5)[/tex]

                     [tex]=(x^2+5x+6)(x-1)(x-5)[/tex]

Now, multiply the next two factors.

                     [tex]=(x^2+5x+6)(x^2-5x-x+5)[/tex]

                     [tex]=(x^2+5x+6)(x^2-6x+5)[/tex]

Now multiply these two factors.

                    [tex]=x^2(x^2-6x+5)+5x(x^2-6x+5)+6(x^2-6x+5)[/tex]

                     [tex]=x^4-6x^3+5x^2+5x^3-30x^2+25x+6x^2-36x+30[/tex]

                     [tex]=x^4-x^3-19x^2-11x+30[/tex]

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Answer:

75%

Step-by-step explanation:

you have to divide 135 by 180 which you look like, 135/180. then once you receive a decimal/fraction which would be .75 you can turn that into a percentage which would be 75%. hope this helped

Option C: [tex]f(x)=2^x[/tex] is the function rule.

Explanation:

The sequence is [tex]2,4,8,16, \dots \dots[/tex]

Let us find the common difference of this sequence.

Common ratio = [tex]\frac{4}{2} =2[/tex]

Hence, [tex]r=2[/tex]

Thus, the given sequence is a geometric progression.

To determine the function rule, let us substitute the values in the general formula of GP which is given by

[tex]f(x)=ar^{x-1}[/tex] where [tex]a=2, r=2[/tex]

Substituting we get,

[tex]f(x)=2(2)^{x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2\times2^x\times2^{-1[/tex]

Adding the powers, we get,

[tex]f(x)=2^{1+x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2^x[/tex]

Hence, the function rule is [tex]f(x)=2^x[/tex]

Thus, Option C is the correct answer.

Answer:

5 - 1 = 4

Step-by-step explanation:

Answer:

The missing side is 7

Step-by-step explanation:

The smaller triangle has the same exact angles and the bigger one. If you notice each side with a value is three times the smaller one. 8m times three equals 24m. So if we divide 21 by 3 we get 7

Answer: 7

Step-by-step explanation:

Answer:

I = 0.015x

Step-by-step explanation:

To calculate the interest obtained from your investment after one year, multiply the interest rate by the investment.

You can use the formula I = Prt; where:

"I" is interest (Capital i).

"P" is principal, starting money or investment.

"r" is the interest rate converted to decimal form.

"t" is the time, usually in years.

Convert 1 1/2% to decimal form. First, change the mixed fraction percentage to a decimal percentage. Convert the percentage to decimal form by dividing by 100. This value will be "r". (Don't confuse decimal form with decimal form as a percentage).

1 1/2% = 1.5%

1.5% ÷ 100 = 0.015

r = 0.015

From the problem, we know the time is 1 year; t = 1.

We don't know the value for the principal, "P", but we are told to use the variable "x"; P = x

Using the bolded information, substitute them for the variables into the formula.

I = Prt

I = (x)(0.015)(1)     Remember any number multiplied by "1" is not changed.

I = (x)(0.015)       Change the standard formatting without brackets.

I = 0.015x         Formula for the interest obtained after 1 year.

Interest obtained after 1 year in dollar is 0.015x

Given that;

Number of year = 1

Number of dollars invested = x

Rate of interest = [tex]1\frac{1}{2}[/tex]%

Find:

Interest obtained after 1 year

Computation:

Rate of interest = [tex]1\frac{1}{2}[/tex]%  = 3/2 % = 1.5% = 0.015

Interest = (P)(R)(T)

Interest obtained after 1 year = (x)(1)(0.015)

Interest obtained after 1 year = 0.015x

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Answer:

(2m)^3(m^4)^5= 8m^23

(-3y^5)^3x2y^2= -54y^17

Step-by-step explanation:

1.  For solving first part

  (2m)^3(m^4)^5

   =[tex](2^3 m^3) (m^{20} )\\Acoording \,to\,exponential\,rules \, exponent 4 \, and\, 5 \,were\, \,multiplied\\As\\\2^3 =8 \\so\\8m^3 \times m^{20} \\\\Acoording \,to\,exponential\,rules \, exponent \,3 \,and\,20\,will\,be\,added\\x^{2} 8m^{23}[/tex]

(2m)^3(m^4)^5= 8m^23

2. For solving second part

(-3y^5)^3 x 2y^2

[tex](-3^3) y^{5\times3} \times 2y^2\\\\As \,3^3= 27 \,and\\\\applying \,exponential\, rule \,the\, exponents\ 5 \, and\, 3 \,will\,be\,multiplied\\the \,equation will become\\-27 \,y15 \times 2y^2\\\\applying \,exponential\, rule \,the\, exponents\, 15 \,and\, 2 \,wil, be\,added \\-54 y^{17}[/tex]

(-3y^5)^3 x 2y^2= -54y^17

Keywords: Algebra

Learn more about algebra at:

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Answer:

The system of inequalities is given by

i) x + y ≥ 10

ii) 9x + 4y ≤ 100

Step-by-step explanation:

i) let x be the number of grams of fat in the non-carb brownie.

ii) let y be the number of grams of protein in the non-carb brownie.

iii) The brownie must weigh at least 10 grams

iv) therefore we can write x + y ≥ 10

v) The brownie must have no more than 100 calories

vi) therefore we can write 9x + 4y ≤ 100

Answer:

112 will have been paid for their trip

Step-by-step explanation:

You have to divide $3920 by $35 to get your answer

Answer:

64

Step-by-step explanation:

pemdas says parenthesis first

3+5=8

8(8)

8 times 8 equals 64

We can add the numbers inside the parenthenses: 8(3+5)=8(8)

Now just multiply and we get 64.

So 64 is the simplified answer

Hope this helped!

Rate of commission as a percent is 12 %

Solution:

Kara weekly paycheck is $6,500 including her salary which is $1,000

Therefore,

Commission amount = Weekly paycheck - salary

Commission amount = 6500 - 1000

Commission amount = 5500

Her sales for the week totaled to $45,000

Therefore rate of commission is given as:

[tex]Commission\ rate = \frac{\text{commission amount}}{\text{sales for week}} \times 100[/tex]

Substituting the values we get,

[tex]Commission\ rate = \frac{5500}{45000} \times 100\\\\Commission\ rate = \frac{550}{45}\\\\Commission\ rate = 12.2 \approx 12[/tex]

Thus rate of commission as a percent is 12 %

Answer:

V=-27

Step-by-step explanation:

8v+1=7v-26

-7v -7v

v+1=-26

-1 -1

v=-27

Answer:

2 5/8 to 1.

Step-by-step explanation:

That would be 1  3/4 divided by 2/3.

= 7/4 / 2/3

= 7/4 * 3/2

= 21 / 8

= 2 5/8

Answer 2 5/8 to 1.

I think

Answer:

84.82 ft³

Step-by-step explanation:

Answer:

84.823

Step-by-step explanation:

The formula of the volume of cone is v= 1/3 (PI* r^2) h

We have that h= 9feet , and r= 3

So, v =1/3 (Pi * 3^2) 9

V=84.82300

Answer:

  the net amount is due in 45 days

Step-by-step explanation:

Invoice terms often have a discount for early payment, and a specification as to the date by which payment in full is expected. n/45 means the net amount of the invoice is due in 45 days.

Option A. When m increases , n tends to increase.

Step-by-step explanation:

Positive correlation is a relationship between two variables in which both variables move in the same direction.

Option A. When m increases , n tends to increase.

Answer:

A. When m increase, n tends to increase

Answer: 47 degrees

Step-by-step explanation: If it dropped form 35 to 0. That is 35 degrees, if it dropped from 0 to -12 degrees that is 12 more degrees. 35 + 12 = 47

Answer:

it dropped 47°

add 12 to 35

Answer:

[tex]\$ 36000\ down\ payment\ is=30\%\\\\\$ 42000\ down\ payment\ is=35\%[/tex]

Step-by-step explanation:

[tex]Purchase\ price=\$ 120000\\\\[/tex]

[tex]when\ down\ payment=\$ 36000\\\\percentage\ down\ payment=\frac{down\ payment}{total\ amount}\times 100\\\\percentage\ down\ payment=\frac{36000}{120000}\times 100\\\\percentage\ down\ payment=0.3\times 100=30\%[/tex]

[tex]when\ down\ payment=\$ 42000\\\\percentage\ down\ payment=\frac{down\ payment}{total\ amount}\times 100\\\\percentage\ down\ payment=\frac{42000}{120000}\times 100\\\\percentage\ down\ payment=0.35\times 100=35\%[/tex]

Final answer:

A $36,000 down payment is 30% of the $120,000 purchase price. A $42,000 down payment would be 35% of the purchase price.

Explanation:

To calculate what percent the down payment is of the purchase price, we use the formula:

(Down Payment / Purchase Price) x 100 = Percentage of Purchase Price

For the initial $36,000 down payment:

Divide $36,000 by the purchase price of $120,000 to get 0.3.

Multiply 0.3 by 100 to get 30%.

Therefore, a $36,000 down payment is 30% of the $120,000 purchase price.

For a $42,000 down payment:

Divide $42,000 by the purchase price of $120,000 to get 0.35.

Multiply 0.35 by 100 to get 35%.

A $42,000 down payment would be 35% of the purchase price.

Answer:

Divide 11 by 10 . Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (1) by the divisor 10 . Subtract 10 from 11 . :) Hope this helps!

It can be a fraction of 11/10 as a mixed number is 1 1/10.

To convert a fraction into a mixed number, you need to divide the numerator (top number) by the denominator (bottom number).

The whole number part of the result is the whole number of the mixed number, and the remainder becomes the numerator of the fractional part.

As per the question, we have the fraction 11/10.

Dividing 11 by 10 gives:

11 ÷ 10 = 1 remainder 1

So the whole number part is 1, and the fractional part is 1/10. We can express this as a mixed number by writing:

11/10 = 1 1/10

Therefore, 11/10 as a mixed number is 1 1/10.

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Answer:

y = - 2x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2, thus

y = - 2x + c ← is the partial equation

To find c substitute (3, 2) into the partial equation

2 = - 6 + c ⇒ c = 2 + 6 = 8

y = - 2x + 8 ← equation of perpendicular line

Answer:

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates.

Answer:

1)  (4,6),(-4,6), (4,12),(-4,12)

2) (4,9) or (-4,9)

Step-by-step explanation:

Observe that the two vertices given, (0,6) and (0,12) are on the y-axis.

The distance between this points is |12-6|=6

We know area of a triangle is [tex]A=\frac{1}{2}bh[/tex]

We were given area as 12.

[tex]\frac{1}{2}*b*6=12[/tex]

[tex]3b=12[/tex]

b=4 units

We can find a point 4 units horizontally away from any of the vertex.

So (4,6),(-4,6), (4,12),(-4,12) are feasible vertices.

For the triangle to be isosceles, then the third vertex must be on the horizontal line through the midpoint of (0,6) and (0,12) and must be 4 units away from the line x=0.

Therefore if thr triangle is isosceles, then third vertex must be at (4,9) or (-4,9)

Answer:

2) D

12) C

13) D

Step-by-step explanation:

2)     4° C at 6:00 PM

A)  + 2°  - 6° = - 4°          4°  -  4°  = 0°       0° does not equal 4°        A  [tex]\neq[/tex] Correct

B)   - 5°  + 1° = - 4°           4°  -  4°  = 0°       0°  does not equal 4°      B  [tex]\neq[/tex] Correct

C)  + 6° - 4° =  + 2°          4° + 2° = 6°           0° does not equal 4°      C  [tex]\neq[/tex] Correct  

D)  - 7°   + 7° = 0°            4°  + 0°  = 4°          4°  does equal 4°           D = Correct

The answer to question #2 is D

12)  M = -3

N ---->  M = 8.5 units

The only possible options for N are:

-3 + 8.5 = 5.5

-3 - 8.5 = -11.5

-11.5 is not a choice, so the answer to question #12 is C

13)  Scale: 1 inch = 70 yards

Abe walks 3.5 inches (on the diagram)

Multiply both sides of the scale by 3.5

3.5 * 1 inch = 70 * 3.5

3.5 inches = 245 yards

Abe walked 245 yards

The answer to question #13 is D

Hope this helps :)