Find the values of a and b if 5+3√3/7+4√3 = a + √3b

Step-by-step explanation:

area of rectangle= 12×6

=72ft^2

A2=9ft^2 whereby the base of the hole is 3ft

height is 6ft

therefore the square is 18 ft

Answer:

4th option

Step-by-step explanation:

the solution is at the point of intersection of the 2 lines, that is

(- 2, 4 ) where x = - 2 , then

f(- 2) = g(- 2)

Answer: D. or f(–2) = g(–2)

Step-by-step explanation:
In the given graph, the two lines intersects at x = -2

And intersection point is that point, where the y values of the two graphs are equal.

That is: f(x) = g(x)

And at x=-2, the y values are equal. So:

f(-2) = g(-2)

Answer:

4^-3*(1/4)^2

(1/64)*(1/16)

=(1/1024)

Answer:

0.00025

Step-by-step explanation:

hope it'll help I'll ask . if you feel that it's not that correct please comment so that I can ask my sister who I'm sure she'll help although she's far good day.

Answer:

3xy-2x

Step-by-step explanation:

Distribute x to both 3y and -2: 3y*x-2*x.

The given statement is false.

What is the effect of a row operation on a determinant?

The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.

Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.

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Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50

Points given for every correct Answer = +3

Points deducted for every Incorrect Answer = -1

For every question unanswered ,

points Deducted = -0.5

Total Points Obtained by Desiree after Answering all the questions = 110

Number of Answers that Desiree answered correctly = x questions

Number of Incorrect Answers = (50 - x) questions

Then,the Equation representing above situation

→ 3 × x + ( -1 ) × ( 50 - x ) = 110

⇒3x - 50 + x = 110 ----------- equation that represents the given situation

⇒ 4x - 50 = 110

Adding 50, on both sides

→ 4x - 50 + 50 = 110 + 50

⇒ 4x = 160

Dividing both sides by, 4 we get

x = 40

Number of correct answers given by Desiree= 40 questions

Number of Incorrect Answers = 50 - 40

= 10 Questions .

Answer:

Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.

If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is

3(50 - x) + x = 110

and the equation will have

no solution

.

Step-by-step explanation:

Answer:

195

Step-by-step explanation:

87+38+40=165

360-165=195

Hope this helps!

If not, I am sorry.

Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]

Step-by-step explanation:

The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.

Linear function that is represented by the graph is f(x)= -1/2 x+1.

Here, we have,

From the graph,

y - intercept of the linear function is 1 , i.e. c = 1

and there are two points on the line (-4, 3), (4, -1)

We can get the equation of line by applying slope-intercept formula,

Slope of the line,

m = y₂ -y₁ / x₂-x₁

so, we get,

m = -1 -3 / 4 + 4

   = -4/8

   = -1/2

Now applying slope-intercept formula,

y = mx+c

Putting the values,

=> y = -1/2 x + 1

=>f(x) = -1/2 x + 1.

Therefore, linear function that is represented by the graph is

f(x) = -1/2 x + 1.

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Answer:

[tex](x+5)(x+2)[/tex]

Step-by-step explanation:

[tex]\textbf{Given that,}\\\\~~~~x^2 +7x +10\\\\=x^2 +5x +2x +10~~~~~~~~~~~~~~~~~~~~;\textbf{Rewrite}~ 7x ~ \textbf{as}~ 5x +2x\\\\=x(x+5) +2(x+5)\\\\=(x+5)(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Take out the common factor}~ x+5[/tex]

The simplified product of [tex]2\sqrt{5x^{3} }[/tex] and -3[tex]\sqrt{10x^{2} }[/tex] is -30[tex]x^{5/2} \sqrt{2}[/tex].

Given Two expressions: -3[tex]\sqrt{10x^{2} }[/tex] and 2[tex]\sqrt{5x^{3} }[/tex].

We have to multiply both the expressions and it can be done as under:

-3[tex]\sqrt{10x^{2} }[/tex] *2[tex]\sqrt{5x^{3} }[/tex]

Firstly we have to multiply -3 with 2 to get

=-6[tex]\sqrt{10x^{2} }\sqrt{5x^{3} }[/tex]

Then we have to find square root of x cube and x square which is x to the power 3/2 and x to the power 1.

=[tex]-6x^{3/2} x\sqrt{10}\sqrt{5}[/tex]

Now we have to multiply both the numbers in the root to get the answer;

=-6[tex]x^{5/2} \sqrt{50}[/tex]

Square root of 50 is 5 root 2.

=-6*5[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]

=-30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]

Hence the simplified product is -30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex].

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A percentage is a way to describe a part of a whole. The amount Emily shared is $30.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,

15% of $200

= 0.15 × $200

= $30

The amount Emily shared is $30.

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Answer:

1.00 + [(n - 1) × 0.20]

or

0.80 + [n × 0.20]

Step-by-step explanation:

week 1: 1.00

week 2: 1.20

week 3: 1.40

we could rewrite this as:

week 1:  1.00 + [0 × 0.20]

week 2: 1.00 + [1 × 0.20]

week 3: 1.00 + [2 × 0.20]

we can write this overall as:

week __ : 1.00 + [x × 0.20]

> x being the amount of weeks that have passed since week 1

but, we need to express this as in terms of nth, so, we need to figure out how the week is related to the x value

each week, we subtract 1 from the week number [to account for week 1]

so, we can write this as: 1.00 + [(n - 1) × 0.20]

or, we can backtrack from the first week, and start our counting at 0.80:

0.80 + [n × 0.20]

we can test this out:

(week 1)

1.00 + [(n - 1) × 0.20]

1.00 + [(1 - 1) × 0.20]

1.00 + [0 × 0.20]

1.00

or...

(week 1)

0.80 + [n × 0.20]

0.80 + [1 × 0.20]

0.80 + 0.20

= 1.00

So, nth week should be expressed as either:

1.00 + [(n - 1) × 0.20] or

0.80 + [n × 0.20]

(the second one is a little bit more simplified, but it depends on how you're supposed to write it)

hope this helps!!

Answer:

24 ft.

Step-by-step explanation:

Radius = 4 ft

Central angle = 6°

Arc length = radius × central angle

= 4 × 6°

= 24 ft.

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]

      [tex]=142506[/tex]

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]

where;

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]

[tex]\mathbf{^nC_r = 142506}[/tex]

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Answer:

The second option

Step-by-step explanation:

If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4

The answer is option D which is the range will be ( -∞, ∞ ).

After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).

Given function is

u(x) = -2x²+3 and v(x) = ( 1 / x ).

The product of the function will give uv(x).

uv(x) = (-2x²+3 ) x  [tex]\dfrac{1}{x}[/tex]

uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]

When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.

Therefore the answer is option D which is the range will be ( -∞, ∞ ).

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Answer:

$6847.955

Explanation:

Use the compound interest formula, but the value decreases over time.

[tex]\sf A = P(1 - \dfrac{r}{100} )^t[/tex]

where 'A' is final amount, r is rate, t is time

Inserting P = $15,000, r = 23, t = 3 years

[tex]\sf A = 15000(1- \dfrac{23}{100} )^3[/tex]

[tex]\sf A = 6847.995[/tex]

Hence the value of truck after three years will be $6847.955.

Answer:

A wave period is the measure of the time it takes for the wave cycle to complete.

The period of the wave is 2 seconds.

[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]

Explanation:

Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0

Here given:

Apply quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]

Insert values:

[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]

[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]

[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]

Apply quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]

[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]

The probability of selecting a jack, replacing the card, and then selecting a king is 1/169

In a standard deck of cards, we have:

Total = 52

Jack = 4

King = 4

The probability of each is:

P(Jack) = 4/52

P(King) = 4/52

So, we have:

P = 4/52 * 4/52

Simplify

P = 1/13 * 1/13

Evaluate

P = 1/169

Hence, the probability is 1/169

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Answer: [tex]\frac{1}{2} \frac{2}{17} \frac{7}{12}[/tex]

Step-by-step explanation:

When leading coefficient is 1 , the root will be an integer for g(x) = 0

Option 4 is the right answer.

Functions of independent variable in which the variable can appear more than once with different powers.

[tex]\rm g(x) = a_n x^n + a_{n-1}x^{n-1} + ................+ a_o[/tex]

Let this represents the polynomial function

where [tex]\rm a_n \; is\;the \;leading \; coefficient \; a_o \; is \;the\;last \;term[/tex]

Then the according to rational root theorem ,

The root of the function is given by

[tex]\rm \dfrac{p}{q} = \dfrac{factor \;of\; the\; last\; term}{factor \;of \;the\; leading coefficient}[/tex]

So when leading coefficient is 1 , the root will be an integer for g(x) = 0

Option 4 is the right answer.

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Answer:

6 to 9 meals

Step-by-step explanation:

9 If he feeds 2 pounds per meal. 18÷2 =9

6 if he feeds 3 pounds per meal. 18÷3=6

The fraction of their student loan will be left to spend is half of their loan.

A number expressed quotient, in which numerator is divided by denominator is called a fraction.

Let the loan amount be $100.

Expenses for food is given that two fifths of their loan

i.e.

= 2/5 × 100

= $40

Now,

Remaining part will be = $100- $40 = $60

So,

Expenses for travel are given that one sixth of their loan,

i.e.

= 1/6 × 60

= $10

So,

Remaining part will be = $60 - $10 = $50

Hence, the fraction of their student loan will be left to spend is half of their loan.

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Answer:

90

Step-by-step explanation:

Add up all the numbers in the data set and divide that number by the amount of numbers in the data set

85 + 97 + 84 + 88 + 95 + 100 + 81 = 630

630/7 = 90

The Recursive formula for an Arithmetic Sequence is a1 = -3, an = an-1 + 6.

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

Given:

an = -3 + 6(n – 1)

a1= -3

a2= 3

a3 = 9

Here the common difference is 6 and first term is -3

Hence, the recursive formula is a1 = -3, an = an-1 + 6.

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A quadratic equation is in the form of ax²+bx+c. The correct option is C, All the positive solutions.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The graph of the question is given below. Since a quadratic equation has only two solutions, and this two solutions can be found by observing the graph. The coordinate at which the graph of the equation intersect the x-axis are the solution of the equation.

As it can be observed in this graph, that the graph intersect the x-axis at (1,0) and (2,0).Therefore, the solutions of the graph are 1 and 2.

Thus, both the solutions are positive or it can be concluded that all the solutions are positive.

Hence, the correct option is C, All the positive solutions.

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Answer:

B. All solutions that lie on f(x)

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

0.86 ppg

Step-by-step explanation:

25% of 1.15 = 0.25 × 1.15 = 0.2875

1.15 - 0.2875 = 0.8625

Answer:

The answer is incorrect because the slope formula was used incorrectly in step 1 (parentheses weren't used during the substitution and/or the wrong values were substituted).

y=4x-6

Step-by-step explanation:

The equation we're looking for in slope intercept form looks like [tex]y=mx+b[/tex], where "m" is the slope, "b" is the y-coordinate of the y-intercept, and "x" and "y" are variables that have a certain mathematical relationship through this equation.

To find the equation itself, it usually is easier to find slope before finding the y-intercept.

There are many ways to represent slope (usually represented by the letter m), and while they all mean the same thing, they look different, some examples are shown below:

[tex]m=\frac{rise}{run} =\frac{\text{horizontal change}}{\text{vertical change}}=\frac{\Delta{y}}{\Delta{x}} =\frac{\text{change in }y}{\text{change in }x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this problem, since we are given ordered pairs, probably the most useful version will be the last one:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the values from the ordered pairs, it's important to remember that the ordered pairs are (x,y)... that the first coordinate is an x (and will go into the denominator, or bottom, of the fraction), and the second coordinate is a y (and will go into the numerator, or top of the fraction).

It actually doesn't matter which point we choose to be point 1, and which point we choose to be point 2.  For the least amount of confusion, I choose the first point they gave to be point 1, and the second point they gave to be point 2.

So, [tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex]

If I could give only one piece of advice, it would be "ANY time you substitute, use parentheses."  You can always simplify later, but for the initial substitution, keep them (this is why the "mistake" happened in this problem, and is the thing we need to fix).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{(6)-(-2)}{(3)-(1)}[/tex]

Simplifying...

[tex]m=\frac{(6)+(2)}{(3)-(1)}[/tex]

[tex]m=\frac{8}{2}[/tex]

[tex]m=4[/tex]

Thus, the equation we want in slope intercept form, with the new information we know plugged in, looks like this:

[tex]y=(4)x+b\\y=4x+b[/tex]

"b" is still the y-coordinate of the y-intercept (which we don't know yet), and "x" and "y" are variables related through this mathematical equation.

With "m" solved for, we can solve for the "b" by using the relationship in the equation we have so far.

We know that every "x" and "y" ordered pair is an "x" related to the "y" by this specific equation.  Even though we don't know the specific value of "b", we know that the equation must be true for every ordered pair on the line.

While we don't know many associated "y" values and "x" values (for instance, we don't know what the "y" value is when the x is 10, and we don't know what the x value is the "y" is 26), we do know two associations for sure... from the two ordered pairs

[tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex], so

 [tex]x=1 \text{ is related to } y=-2[/tex], and [tex]x=3 \text{ is related to } y=6[/tex]

... and they're related through this equation that we've almost found!

Now, in our equation, there is only room to associate one x and y value at a time, so we need to pick one known association, and substitute those values in.  Since this equation is supposed to relate the x to the y, it should be true for both points (so, we can try both, and it should work out the same.  If you don't want to try both, if you see one ordered pair that has numbers that look easier, use that one):

Substituting Point 1 to find b

[tex]y=4x+b[/tex]

[tex](-2)=4(1)+b[/tex]

simplifying the right side, 4*1 is 4...

[tex](-2)=4+b[/tex]

subtracting 4 from both sides of the equation, and simplifying the left hand side

[tex]-2-4=b\\-2+-4=b\\-6=b[/tex]

Substituting Point 2 to find b (not necessary, but a good double-check)

[tex]y=4x+b[/tex]

[tex](6)=4(3)+b[/tex]

simplifying the right side, 4*3 is 12...

[tex]6=12+b[/tex]

subtracting 4 from both sides of the equation, and simplifying the left hand side

[tex]6=12+b\\6-12=b\\6+-12=b\\-6=b[/tex]

So, as a verification, we get the same value of b (which we should have, because this equation is supposed to work for every pair of (x,y) that has this relationship, and those were the only two points that we knew that did).

Substituting the value we found for b:

[tex]y=4x+(-6)[/tex]

...and simplifying...

[tex]y=4x-6[/tex]