Solve each system by graphing.

Answer:

There is 10% error in both minimum and extreme values i.e. 120 & 140 , Error in 120 is 10% i.e. = 12, Since value can be more or less in error ∴ Error in 120 is ±12.

Answer:

4% and 5% respectively

Step-by-step explanation:

Let the intrest rate be x in the first account at x% and (x+1)% in the second account.

ATQ, 100=(x)*1500/100+(x+1)*800/100

x=4.

The domain of a set is the possible input values the set can take.

It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers

Given that: ∀x ∃y(x+y≥0)

Considering x+y ≥ 0, it means that the values of x + y are at least 0.

Make y the subject in x+y ≥ 0

So, we have:

[tex]\mathbf{y \le -x}[/tex]

There is no restriction as to the possible values of x.

This means that x can take any real number.

Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.

Read more about domain at:

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Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

                                                           = [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]

Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.

Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]

                                         = 364 square inches

Therefore, area of the metal sheet required = 364 square inches

Answer:

160

Step-by-step explanation:

(3a+4b) = 16

ab = 4

Square (3a+4b)

(3a+4b)(3a+4b) = 16^2

9a^2 + 12ab+12ab+16b^2 = =256

9a^2 +16b^2   +24ab=256

9a^2 +16b^2   +24ab - 24 ab=256 -24ab

9a^2 +16b^2  =256- 24ab

We know ab = 4

9a^2 +16b^2  =256- 24*4

9a^2 +16b^2  =256- 96

9a^2 +16b^2  =160

Answer:

if we do 9 times a number that will be

9x

Answer:

9x

Step-by-step explanation:

9 times a number (a variable)  = 9x

Answer:

51 cents for 17 inches of wire

Step-by-step explanation:

22 = 66

17 = x

22x = 66 * 17

22x = 1122

x = 51 cents

or

22 inches costs 66 cents

1 inch costs 3  cents (66 / 22 = 3  cents)

17 inches costs 51  cents (17 * 3 = 51 cents)

Answer:

a) 10,025 m = 10km 25m = 10.025 km

b) 1,500 m = 1 km 500 m = 1.5 km

Answer:

a) 10025m = 10km 25m = 10.025km

b) 1500m = 1km 500m = 1.5km

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit conversion.

Unit conversion is the conversion between different units of measurement for the same quantity.

1 km = 1000 m

Solve:

a)

b)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1.009823361

Step-by-step explanation:

Just divide like this:

[tex] \frac{100.331}{99.355} = 1.009853361[/tex]

Answer:

-6k = -8 is an expression

A and C are inequalities

D is arithmetic

Answer:

[tex]f(3x)=9x^2-3[/tex]

Step-by-step explanation:

One is given the following function:

[tex]f(x)=x^2-3[/tex]

One is asked to evaluate the function for ([tex]f(3x)[/tex]). Substitute ([tex]3x[/tex]) in place of ([tex]x[/tex]) then simplify. Remember that a number raised to an exponent is the same as that number times itself the number of times that the exponent indicates. One can apply this logic here while simplifying,

[tex]f(x)=x^2-3[/tex]

[tex]f(3x)=(3x)^2-3[/tex]

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

[tex]f(3x)=(9x^2)-3[/tex]

[tex]f(3x)=9x^2-3[/tex]

Answer:

AA

Step-by-step explanation:

See In Triangle ABC and Triangle STU

[tex]\because\begin{cases}\sf \angle A=\angle S=90° \\ \sf \angle B=\angle T=31°\end{cases}[/tex]

Hence

[tex]\sf \Delta ABC~\Delta STU(Angle-Angle)[/tex]

By AA similarity  triangle ABC is similar to triangle SUT. Therefore, option A is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

In the given triangle ABC, ∠C=180°-90°-31°

∠C=59°

In the given triangle SUT, ∠U=180°-90°-31°

∠U=59°

Here, ∠B=∠T (Given)

∠C=∠U (Obtained using angle sum property of a triangle)

So, by AA similarity ΔABC is similar to ΔSUT.

Therefore, option A is the correct answer.

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Answer: 205.3

I suppose all measures of angles are done from the same axis (for example x-axis)

Step-by-step explanation:

You just have to use the theorem of Al'Kashi:

[tex]d^2=400^2+300^2-2*300*400*cos(30^o)\\\\d\approx{205.3(km)}[/tex]

Answer:

Step-by-step explanation:

The number which is divisible by 2, 3, 4, 5 and 6 will also be divisible by LCM of 2, 3, 4, 5 and 6. Let us divide 9999 by 60 and find the remainder, Remainder after dividing 9999 by 60 is 39. Therefore, the largest number which is divisible by these numbers should be 39 less than 9999.

Answer:

k=3

Step-by-step explanation:

Assuming the centre of dilation is 0,0, we can use the formula (kx,ky) to determine it.

Here,

The co-ordinates of pre-image=(0,1),(-1,-1) & (1,-1)

The co-ordinates of image=(0,3),(-3,-3) & (3,-3)

Now,

(kx,ky)=(0,3)

(k*0,k*1)=(0,3)

Equating,

k=3

You can use the other coordinates to further solidify your answer.

Answer:

000023 because if we take three 0's we can get 000023 and 417 million

Answer:

c.145.3 to 154.7.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.

The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.

Thus the correct answer is given by option c.

We need to find the percent, let's start but making the equation.

The price is 2.69

The tax cost is 0.13

So what percent of 2.69 is = 0.13.

Equation: X/100 x 2.69 = 0.13

Multiply each side by 100 so we can get x alone with the price: 2.69x = 13

Now to get x alone, we must divide both sides by 2.69: x = 4.8

Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.

I hope this helps! :)

Answer:

0.127

Step-by-step explanation:

Answer:

n = -10

Step-by-step explanation:

1 / 8^n  = 8^5^2

We know that 1/a^b = a^-b

We also know that a^b^c = a^(b*c)

8^-n = 8^(5*2)

8^-n = 8^(10)

Since the bases are the same, the exponents are the same

-n = 10

n = -10

Answer:

10a²+17a²s-6s²

Step-by-step explanation:

(-2a²+s)(5a²-6s)

= -10a²+12a²s+5a²s-6s²

= -10a²+17a²s-6s²

Answer:

b

Step-by-step explanation:

==========================================================

Explanation:

Piecewise functions are admittedly a bit confusing at first if you aren't familiar with them.

However, they aren't too bad. Effectively we have two functions going on depending on what the input is.

If the input x is less than 0, then we go for the top row and say [tex]f(x) = x^2[/tex]

OR

If the input x is greater than 0, then we go for the bottom row to say [tex]f(x) = \sqrt[3]{x}[/tex]

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

In this case, the input is x = -8. So we go for the first row since this x value satisfies x < 0.

We would then say:

[tex]f(x) = x^2\\\\f(-8) = (-8)^2\\\\f(-8) = 64\\\\[/tex]

Which points us to choice A as the final answer.

Answer:

f(-8) = 64

Step-by-step explanation:

Input -8 into one of the formulas (either will work) and the answer should be 64. therefore, if x is -8, f(-8) would equal 64.

Answer: D

Step-by-step explanation:

(lines parallel to each other have the same slope)

slope = m = 2

y = mx + b, (5,6)

6 = 2(5) + b

6 = 10 + b

b = -4

y = 2x - 4

y - 6 = 2(x - 5)

y - 6 = 2x - 10

y = 2x -4

Given:

The equation of a parabola is:

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

To find:

The coordinates of the vertex of the given equation.

Solution:

The vertex form of a quadratic function is:

[tex]y=a(x-h)^2+k[/tex]               ...(i)

Where, a is a constant and (h,k) is the vertex.

We have,

[tex]y=(x+2)^2-1[/tex]                 ...(ii)

On comparing (i) and (ii), we get

[tex]a=1[/tex]

[tex]h=-2[/tex]

[tex]k=-1[/tex]

We know that the vertex of the parabola is (h,k).

Therefore, the vertex of the given equation is (-2,-1).

[tex]\\ \sf\longmapsto (f+g)(x)[/tex]

[tex]\\ \sf\longmapsto f(x)+g(x)[/tex]

[tex]\\ \sf\longmapsto 4x-3+9x+2[/tex]

[tex]\\ \sf\longmapsto 4x+9x-3+2[/tex]

[tex]\\ \sf\longmapsto 13x-1[/tex]

Answer:

13x - 1

Step-by-step explanation:

f(x) + g(x) = 4x - 3 + 9x + 2

f(x) + g(x) = 4x+9x + 2 - 3

f(x) + g(x) = 13x - 1

9514 1404 393

Answer:

  g, h, f

Step-by-step explanation:

A graph of two exponential curves will have the one with the least growth rate crossing under the one with the greater growth rate. Here, f(x) is shown crossing under g(x) and is on its way to a point of intersection with h(x). So, f(x) has the least growth rate.

g(x) and h(x) start out at about the same level, but g(x) curves upward faster, indicating it has the higher growth rate.

In order from greatest to least growth rate, the functions are ...

  g(x), h(x), f(x)

9514 1404 393

Answer:

  C, D, E

Step-by-step explanation:

Vertical asymptotes are found where the denominator is zero. The denominator will be zero when any of its factors is zero. Then the vertical asymptotes are ...

  x = 0   ⇒   x = 0 . . . . . . choice E

  x -1 = 0   ⇒   x = 1 . . . . . choice C

  x +5 = 0   ⇒   x = -5 . . . choice D