Please help me asap i will mark branlist please explain

Please Help Me Asap I Will Mark Branlist Please Explain

Answers

Answer 1

Answer:

195in^2 is the correct answer.

Step-by-step explanation:


Related Questions

4 1/2 −5 1/3 ÷(20x−14 2/3 )=1 5/6

Answers

The answer will come out to be x=5/6

Investors buy a studio apartment for $ 120,000. Of this​ amount, they have a down payment of $ 36,000. Their down payment is what percent of the purchase​ price? What percent of the purchase price would ​a $42,000 down payment​ be?

Answers

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.

8v+1=7v-26 find the v

Answers

Answer:

V=-27

Step-by-step explanation:

8v+1=7v-26

-7v -7v

v+1=-26

-1 -1

v=-27

can someone explain to me HOW to solve these problems
(2m)^3(m^4)^5
(-3y^5)^32y^2

plzzzz help

Answers

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

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Three more than the quotient of a number and 5 is equal to 9

Answers

Answer:

The number is 30.

Step-by-step explanation:

x/5+3=9

x/5=9-3

x/5=6

x=6*5

x=30

Final answer:

The number is 30.

Explanation:

The given question is a mathematical equation.

Let's define the number as 'x'. According to the given equation, the quotient of the number and 5, which is x/5, when three is added to it, should be equal to 9. Mathematically, we can write this as:

x/5 + 3 = 9

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 3 from both sides of the equation:

x/5 = 9 - 3

x/5 = 6

To get rid of the fraction, we can multiply both sides of the equation by 5:

x = 6 * 5

x = 30

Therefore, the number is 30.

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Suppose there is a strong positive correlation between m and n. Which of the
following must be true?

Answers

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

You walked to school on 135 days out of 180 days. What percent of the days did you walk?

Answers

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

Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck is $6,500 including her salary which is $1,000. Her sales for the week totaled to $45,000. Express her rate of commission as a percent rounded to the nearest whole number.

Answers

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 %

Can someone please answer this multiple choice questions numbers 2 , 12 and 13 please answer and please please show work

Answers

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 :)

David pays a 20% income tax on his 2,100-month salary. How much does he pay in taxes each year?
Andre Rick and ty were practicing for a track cycling race. Andre- 750 m in 3 minutes Rick 4 minutes 800m, Ty 950 in 5mmintues, who covered the last distance per minute?
A recipe for banana pudding calls for 2/3 cups of sugar for the flour and 1/4 cups of sugar for the meringue topping, how many cups of sugar is required to make that good banana pudding?
A phone originally price at $40 is now $30 what was the percent discount?

Answers

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

13.
If the temperature drops from 35°F
to -12°F, how many degrees did it
change?

Answers

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

A basketball player shoots a basketball with an initial velocity of 15ft/sec. The ball is released from an initial height of 6.5 feet. The function h(t)=-16t^2+v0t+h0 models the height,in feet, of an object after t seconds. v0 is the initial initial height of the object

part one right function that models the height of the basketball use your function to answer part 2 through 4

part 2 how long does it take for the basketball to hit the ground round your answer to the nearest hundredth show all your work

part 3 when does the basketball reaches maximum height round your number to the nearest hundredth show all your work and explain your answer

what is the maximum height of the basketball round your answer to the nearest hundredth and show all your work and explain your answer

PLEASE HELP

Answers

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.

Vicky has baseball practice every 10 days . She starts on May 5 . Will she have practice on May 19? Yes or no and How do you know ?

Answers

Answer:no

Step-by-step explanation:

It'll be may 15th

if She starts on May 5 then there is no practice on May 19.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that Vicky has baseball practice every 10 days

She starts on May 5 .

We have to find whether she has to practice on May 19.

From May 5 the ten days ends at may 15.

So on May 19 the practice is not there.

So no, Vicky does not practice on May 19.

Hence, if She starts on May 5 then there is no practice on May 19.

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A baseball diamond is a square with corners at home plate, first base, second base, and third base. The distance between home plate and first base is 30 yards. What is the area of a baseball diamond?
A.
900 square yards
B.
120 square yards
C.
90 square yards

Answers

Answer:

A: 900 yards

Step-by-step explanation:

im sure... i had the same test question and got it right! pls give me brainliest

Answer:

900 sq. yd.

Step-by-step explanation:

So, we know that the baseball diamond is a square, so we use the equation of a square, A = [tex]a^{2}[/tex]

Since all sides of a square are equal, each is always gonna be 30 yards. So we substitute a for 30

A = [tex]a^{2}[/tex]

A = [tex]30^{2}[/tex]

A = 900 sq. yd.

Which gives you the area of the diamond as 900 sq. yd.

Convert 11/10 into a mixed number​

Answers

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.

How to convert fractions into a mixed number?

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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steps of solving linear equations

Answers

1. figure out the y- intercept
2. see where the x point meets than go up/down at the y, find your cordinats, make a chart of the slope and figure out the expression

in the ordinary dating of invoices,what does n/ 45 means​

Answers

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.

What if the answer to the equation

2+s>=10;s=7

Answers

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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the two vertices of a triangle are (0,6) and (0,12). if the are of the triangle is 12 square units, where can the third vertex be? What if the triangle is also isosceles?

Answers

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)

Two angles are complementary three times the measure of one of the angles is 10° more than the measure of the other angle. find the difference between the measure of the larger angle in the smaller angle

Answers

Answer:

The difference is 40,

Step-by-step explanation:

Complementary angles , x+y =90

so we know angle 1, we call it  3x and angle 2 we call it y= 3x+10

so 3x +10= 90-x

4x=100

x=25

angle 1= 3(25) - 10

y= 65

65-25= 40

Answer:

  40°

Step-by-step explanation:

Let x represent one of the angles, and y represent the other one. Then we have ...

  x + y = 90

  3x = y +10

Substituting for y in the first equation, we have ...

  x + (3x -10) = 90

  4x = 100

  x = 25

  y = 3(25) -10 = 65

The difference between the angles is ...

  y -x = 65 -25 = 40 . . . . degrees

The difference between the angle measures is 40 degrees.

What is the basis of statistical inference

Answers

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.

Ashton makes more than 32 sandwiches for a party. If Ashton cuts each sandwich into two pieces, which inequality represents the total number of pieces, p, he has?
A. p < 64
B. p > 32
C. p < 32
D. p > 64

Answers

The inequality p > 64 represents the total number of pieces he has ⇒ D

Step-by-step explanation:

Let us revise the inequality words

Less than ⇒ <More than ⇒ >At least ⇒ ≥At most ⇒ ≤

∵ Ashton makes more than 32 sandwiches for a party

∴ The number of sandwiches > 32

∵ Ashton cuts each sandwich into two pieces

- That the number of pieces is the number of sandwiches times 2

∴ The number of pieces > 2 × 32

∴ The number of pieces >  64

- The number of pieces is p

∴ p > 64

The inequality p > 64 represents the total number of pieces he has

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Write the simplest polynomial function with the given roots -3,-2,1 and 5

Answers

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].

I need some help with this equation please!

Answers

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

The interest obtained after 1 year on an investment at 1 1/2% simple interest per year; x = number of dollars invested

Answers

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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25) The angle measurements of triangle XYZ are shown in the
diagram below.

What kind of triangle is XYZ?
A) Acute
B) Obtuse
C) Right
D) Equiangular

Answers

C. Triangle xyz is a right angle triangle due to the “y” angle being 90 degrees

Answer:

Right

Step-by-step explanation:

Triangle having ninety degree angle in it is right angle triangle.

Given the sequence 2, 4, 8, , 16,........, where x = 0, 1, 2, 3, .......what is the function rule? f(x) = 2x + 2 f(x) = 2(2)x f(x) = (2x) f(x) = 2

Answers

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.

There was 5 dogs and 1 dog got lost how many dogs are there now

Answers

Answer:

5 - 1 = 4

Step-by-step explanation:

There are 4 dogs left my guy

Can someone please help me I will mark brainliest

Answers

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:

A diet food company is attempting to create a non-carb brownie composed entirely of fat and protein. The brownie must weigh at least 10 grams but no more than 100 calories. Fat has 9 calories per gram and protein has 4 calories per gram. Write and graph a system of inequalities that represents weight, in grams, of protein and fat.

Answers

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

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