Find the values of x and y.​

Answer:

  Andrew failed to change the direction of the inequality

Step-by-step explanation:

You want to know the mistake in Anderw's work solving the inequality ...

  −4(x + 8) + 25 ≤ −2 + 1(x − 50)

−4(x + 8) + 25 ≤ −2 + 1(x − 50)

−4x − 32 + 25 ≤ −2 + 1x − 50

−4x − 7 ≤ 1x − 52

−5x ≤ −45

x ≥ 9

Andrew's mistake was failing to reverse the inequality symbol when dividing by a negative number (-5) at the last step.

__

Additional comment

The last steps of the solution could be written ...

  -5x ≤ -45

  45 ≤ 5x . . . . . . . add 5x+45 to both sides

  9 ≤ x . . . . . . . . . divide by 5 (no reversal of ≤ is needed)

Answer:

Step-by-step explanation:

Given:

2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10

factor it

I used MatLab   roots(x)  to find these so I kinda cheated :P

-2.5,  -2 ,  1

so we know  -2 is a factor and,  then

x+2=0    is a factor

so the "x+2"  answer C)

Answer:

1-5+171

Step-by-step explanation:

Solution of the given inequality -18 + x < 16 is equal to x < 34.

As given in the question,

Given inequality is equal to :

-18 + x < 16

Get the value of the variable x by adding 18 both the side of the inequality we get,

-18 + x + 18 < 16 + 18

Collect all like terms together we get,

⇒ x + (-18 + 18 ) < 34

⇒ x + 0 < 34

Solution of the inequality -18 + x < 16 is given by

⇒ x < 34

For the given inequality -18 + x < 16 the value of variable x is less than 34.

Therefore, solution of the given inequality -18 + x < 16 is  x < 34.

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The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

As per the given,

Percentage of people who notice the speed limit = 84%

The percentage of people who notice the sign and follow the speed limit is 75%.

Therefore, 84% - 75%  = 9% are the percentage speeding and noticed.

Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".

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The total number of tongue depressors and Band-Aids are 56 and 128 respectively.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given that, a medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total,

Let the number of wrapped tongue depressors be w and that of Band-Aids be b,

Therefore,

w+b= 184

0.04w+0.08b = 12.48

w+2b = 312

On solving the equation, by elimination method, we get,

b = 128

Therefore, w+128 = 184

w = 56

Hence, the total number of tongue depressors and Band-Aids are 56 and 128 respectively.

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The runner's speed If a runner traveled a distance of d(h)=/16h4 in time t(h) = 3h^4 - 3h^3 -5h^2 is  4 /3h^2 - 3h -5h.

The concept that will be used to calculate this is the concept of speed which is the ratio of the distance per time which can be expressed as

speed = distance/time

Then we were given distance as d(h)=/16h^4

time as  t(h) = 3h^4 - 3h^3 -5h^2

Speed = [tex]\sqrt{16h^4} /3h^4 - 3h^3 -5h^2[/tex]

Then we will have 4h^2 /3h^4 - 3h^3 -5h^2

then  take h^2 from both the numerator and denominator and then cancel them , then we will have

= 4 /3h^2 - 3h -5h.

Therefore, the first option is correct.

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A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a reflection across the line x = -3 followed by a reflection across the line y = x.

Given that both triangles are congruent, we can infer or deduce that there were no dilations or contractions. Hence, since we are moving in a clockwise direction, we can submit that this was not a rotation but a reflection.

Hence the first sequence of reflection was such that:

∆ABC reflects onto ∆A′B′C′ across the line x = -3; followed by
a reflection across the line y = x.

Note that in geometry, reflection refers to the mirror image of an image. The line through which an image reflects is called the line of reflection.

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Answer:

16

Step-by-step explanation:

(8+2) + (6 − 4) × 3

= 10+6

=16

A golf club costs $342 at retail. The markup rate is 71.4% if the golf store has increased the price by $42.

Given,

The difference in prices is  $342 - $42 = $300

So, we need to find what percentage of 42 is 300

We do this by dividing: 300/42 = 7.14

which is 71.4 %.

So, the markup is  71.4 %.

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The statement which must be true given the premise that; T is the midpoint of RS and V lies between R and T is; Choice A; RV + VT = TS.

It follows from the task content that the answer choice which represents a true statement regarding the given description be identified.

Since it is given that T is the midpoint of RS, it follows that;

RT = TS.

Also, it is given that point V lies between R and T; it therefore obviously follows that the equation which is true about RV and VT is;

RV + VT = RT.

Therefore, since segments RT and TS are equal;

It follows from the substitution property of equality that;

RV + VT = TS.

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Answer:48

Step-by-step explanation:12x4=48

The cost of the sales tax in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The sales tax percentage in Texas = 5 %

                                                          = 5 / 100

                                                          = 0.05

The cost of 1 bag of dog food in Houston = $ 52

Now ,

The sales tax cost is calculated by the equation ,

The sales tax cost =
Sales tax percentage in Texas x cost of 1 bag of dog food in Houston

The sales tax cost = $ 52 x 0.05

                              = $ 2.60

And , the total cost of 1 bag of dog food = cost of 1 bag of dog food in Houston + sales tax cost

Total cost of 1 bag of dog food = $ 52 + $ 2.60

                                                   = $ 54.60

Therefore , the sales tax cost is $ 2.60

Hence , the sales tax cost to pay in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60

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The distance to the point is less than c=10, so the point is inside the circle.

Given that, (a, b) = (5, –2) and c = 10.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

Part A:

Use of the Pythagorean theorem gets you to the equation for a circle in essentially one step:

Sum of squares of sides = square of hypotenuse

(x -a)²+(y -b)² = c² circle centered on (a, b) with radius c.

Part B:

The circle will be defined for values of x in the domain f ± c, and for values of y in the range b ± c.

domain: 5 ± 10 = [5, -5]

Range: -2 ±10 = [8, -11]

Part C:

The distance from point (10, 2) to (a, b)=(5, -2) is

c² = (10-5)² +(-2-2)²

c² = 25+16

c² = 41

c=√41

c=6.4

The distance to the point is less than c=10, so the point is inside the circle.

Therefore, the distance to the point is less than c=10, so the point is inside the circle.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]

The  simple or compound interest will be

a. $120

b. $12,000

c. $15,000

d. $18,000

e. Option B is better as it is giving us more interest.

Formula of total simple interest is

SI = (P * R * T) /100  where

P = initial principal balance

r = annual interest rate

t = time (in years)

Formula of compound interest is

C.I.= P × [tex](1 + r/n)^{nt}[/tex] - P  where

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

a. By applying the formula given above we will get

SI = (3000 * 0.4 * 10) / 100

SI = $120

b. Formula to find total value is P * R * T. By applying this we will get

I = 3000 * 0.4 * 10

I = $12,000

c.  By putting values in the formula we will get

CI = 3000 * [tex](1 + 0.2)^{10}[/tex] - 3000

CI = 18000 - 3000

CI = $15,000

d. formula to find total compound value is P * [tex](1 + r/n)^{nt}[/tex]. By applying this in the formula we get

A = 3000 [tex]( 1 + 0.2 )^{10}[/tex]

A = $18,000

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The resulting value of the the expression 6769 x 925 by first rounding each number so that it has only 1 nonzero digit is 63,000

Round off

Round off refers a number is made simpler by keeping its value intact but closer to the next number. And it is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given,

Here we need to estimate  6769 x 925 by first rounding each number so that it has only 1 nonzero digit.

Here we have to take individual terms to round off then we get,

By rounding 6799 so that it has only one non-zero digit is rounding it to nearest thousand.

6769 rounds to nearest thousand as 7000 as hundreds digit 7 > 5.

Similarly, by rounding 925 so that it has only one non-zero digit is rounding it to nearest hundred.

925 rounds to nearest hundred as 900 as tens digit 2 < 5.

Now, the estimated value after rounding each number so that it has only one non-zero digit is

=> 7000 x 900

=> 63000.

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equation and graph attached

Answer:

14 and 15

Step-by-step explanation:

[tex]196<201<225 \\ \\ \sqrt{196}<\sqrt{201}<\sqrt{225} \\ \\ 14<\sqrt{201}<15[/tex]

Answer:

x=3

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!

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

So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!

2x+3  x-3 those are correct

Kurt spent a total amount of $22.68 a month on movie streaming services.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.

These operations are used from the unit rates, as when we have an amount over some time, then the amount per unit of time is the total amount divided by the total time.

We have been given the important parameters are;

The total amount = is $96.39.

The time is a mixed number, 4 and 1/4 months, hence it will be 4.25 months,

Therefore, his monthly spending is given by the unit rate as;

96.39/4.25 = $22.68 a month.

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The ending balance after 3 years is $1508.34

What is compound interest?

The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.

The compound amount and compound interest are calculated by:

  Compound amount,   [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

  Compound interest, [tex]I = A - P[/tex]

where, P is the principal amount

           r is the rate of interest(in decimal)

           n is the number of  times the interest is compounded annually

           t is the time.

Given, Principal amount, P = $1400

           rate of interest, r = 2.5% = 0.025

           n = 2 (compounded semi-annually)

           t = 3 years

Then, the compound amount is calculated by:

                 [tex]A=1400(1+\frac{0.025}{2} )^{2*3}\\[/tex]

          or,       [tex]A=1400(1+0.0125 )^{6}\\[/tex]

          or,       [tex]A=1400(1.0125 )^{6}\\[/tex]

          or,       [tex]A=1508.34[/tex]

Therefore, the ending balance is $1508.34

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