Consider the graph of rational function f
f(x)
-4
I
T
1
-2
6-
4-
2+
-2-
-4-
-6.
0
4+12
O
N.
2
Which equation represents function ?
OA f(2)= =+
OB. f(2)=426
Oc f(2)==
OD. f(2)=342-6
TY
6
X

-8.(2a - 1) = 36

-16a + 8 = 36

-16a = 36 - 8 = 28

a = 28/(-16) = -7/4

The correct answer is -7/4 = -1.75

The solution to the given equation is [tex]\frac{-7}{4}[/tex].

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.

We have,

Expression -8(2a - 1) = 36

So,

Now,

To get the solution to this expression,

i.e.

-8(2a - 1) = 36

Rewrite it as,

i.e.

Opening Brackets,

We get,

-16a + 8 = 36

Now,

Taking variable terms on one side and other terms on another side,

We get,

-16a = 36 - 8

On solving we get,

-16a = 28

i.e.

a = [tex]\frac{-28}{16} = \frac{-7}{4}[/tex]

So,

The solution to the given equation is [tex]\frac{-7}{4}[/tex].

Hence, we can say that the solution to the given equation is [tex]\frac{-7}{4}[/tex].

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Answer:

Gradient (slope) is 5.

Step-by-step explanation:

To find the gradient (slope) of a curve graph at x = x₁ can be done by steps following:

First, derive the given function which is:

[tex]\displaystyle{y = (\sqrt{x}+3)(3\sqrt{x}-5)[/tex]

Differentiation can be done two ways - go ahead and expand the expression then derive it or you can use the product rule where it states that [tex]\displaystyle{y'=u'v+uv'}[/tex]

I'll be using product rule:

[tex]\displaystyle{y' = (\sqrt{x}+3)'(3\sqrt{x}-5)+(\sqrt{x}+3)(3\sqrt{x}-5)'}[/tex]

Note that the following process will require you to have knowledge of Power Rules:

[tex]\displaystyle{y = ax^n \to y' = nax^{n-1}}[/tex]

Hence:

[tex]\displaystyle{y'=\dfrac{1}{2\sqrt{x}}(3\sqrt{x}-5) + (\sqrt{x}+3)\dfrac{3}{2\sqrt{x}}[/tex]

Now we know the derivative. Next, we find the slope at x = 1 which you substitute x = 1 in derived function:

[tex]\displaystyle{y'(1)=\dfrac{1}{2\sqrt{1}}(3\sqrt{1}-5) + (\sqrt{1}+3)\dfrac{3}{2\sqrt{1}}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(3-5) + (1+3)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(-2) + (4)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=-1 + 2(3)}\\\\\displaystyle{y'(1)=-1 + 6}\\\\\displaystyle{y'(1)=5}[/tex]

Finally, we have found the slope or gradient at x = 1 which is 5.

Please let me know if you have any questions!

Answer: (-2, 1)

Step-by-step explanation:

       We will graph the given equations. The point of intersection is the solution to the system of equations. See attached.

       They intersect at the point (-2, 1) giving us an answer of x = -2 and y = 1, but this question asks for the answer as an ordered pair so we leave it as is.

Answer:

B

Step-by-step explanation:

Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.

This is equal to c(d+b), so:

(1/2)(c)(2d+a+b)=c(d+b)

(1/2)(2d+a+b)=d+b

d+0.5a+0.5b=d+b

0.5a+0.5b=b

0.5a=0.5b

a=b

Answer: y=3

Step-by-step explanation:

The x-axis is on the horizontal line, and the y-axis is on the vertical line. On the horizontal line at -1, just go up until you find where y is located.

By doing this, you can find that y=3.

Answer:

Step-by-step explanation:

All we have to do is find the point on the line where x = -1. If we know this, we can see how high the point is (i.e., find it's y-value). Then, we would know the value of y.

If we draw a vertical line from where x equals -1, we see that it crosses the line at point (-1, 3). This means that we can draw a line from the point to the number -1 on the x-axis and another line from the point to the number 3 on the y-axis.

Hence, the y-value when x=-1 would be 3.

The money supply in the economy is  $1025302.6

Bank loans or invests its excess reserves to earn greater hobby. A one-dollar boom inside the financial base reasons the money deliver to boom through more than one dollar. The growth inside the money supply is the cash multiplier.

The money multiplier is the primary can used to calculate what a change in reserves could do to the money supply. The method for the cash multiplier is 1/r where r is the reserve ratio. once one has calculated the money multiplier, they might then multiply that through the exchange in reserves.

The money multiplier is critical in macroeconomics because it determines the cash supply, which affects interest charges. it is also critical in banking because it impacts economic coverage and the steadiness of the banking region.

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Answer:

Given:

mu = 200 lb, the mean sigma = 25 the standard deviation

For the random variable x = 250 lb, the

z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2

From standard tables for the normal distribution, obtain

P(x < 250) = 0.977

Answer: 0.977

The probability that any given car will have a brake failure if it is make a is 0.0065%

The complete question is added as an attachment

From the table in the question, we have:

P(Brake failure|car a) = 0.0065%

The above represents the required conditional probability

Hence, the probability that any given car will have a brake failure if it is make a is 0.0065%

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Answer: The probability that any given car will have a brake failure if it is making A, is 0.0065%.

Step-by-step explanation:

I got it right on Edmentum!

Answer:

180

Step-by-step explanation:

Solution 1: Any straight line is 180 degrees.

Solution 2: Angle WX=Angle YZW+ Angle YZX

Angle YZW=Angle YZX=90

Angle YZW+ Angle YZX=90+90=180

So Angle WX=180

Answer:

Step-by-step explanation:

You can find WX if you know some special properties of special triangles:

1. A 45-45-90 triangle (a triangle with angle measures of 45°, 45°, and 90°) will have a 1:1:√2 ratio (the legs of the triangle are the same length and the hypotenuse is the length of any leg times √2)

2. A 30-60-90 triangle (a triangle with angle measures of 30°, 60°, and 90°) will have a 1:√3:2 ratio (the hypotenuse is twice the measure of the shorter leg, and the longer leg is √3 times the length of the shorter leg)

For reference, a leg is a side on a right triangle that isn't the hypotenuse.

In this picture, the first type of triangle is on the right, and the second type is on the left.

The shorter leg on the left triangle has a length of 10, and WZ is the longer leg. The longer leg is √3 times the shorter one, so WZ = 10√3

Both legs of a 45-45-90 triangle have the same measure, so ZX is 10.

Since WX is made up of WZ and ZX, it's length is the sum of both lengths.

[tex]{\rm WX} = 10\sqrt{3}+10[/tex]

[tex]{\rm WX} \approx 27.321[/tex]

The value of the probability P(A and C) is 0.18

The complete question is added as an attachment

From the attached tree diagram, we have:

P(A) = 0.6

P(C) = 0.3

The required probability is then calculated as:

P(A and C) = P(A) * P(C)

This gives

P(A and C) = 0.6 * 0.3

Evaluate

P(A and C) = 0.18

Hence, the value of the probability P(A and C) is 0.18

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Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

and the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides opposite of their associated angles (A, B, C).

1)

17/sin(26) = 12/sin(C)

sin(C) = 12×sin(26)/17 = 0.309438457...

C = 18.02539254...° ≈ 18°

3)

180 = 27 + 115 + C

C = 38°

19/sin(38) = AC/sin(27)

AC = 19×sin(27)/sin(38) = 14.01065332... in ≈ 14 in

In first triangle side angle m∠C is 18° and in first triangle side AC is 14 in. This can be obtained by using the law of sine.

We know the law of sine which is,

If in a triangle, Δ ABC,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex], where a is the side opposite to the angle m∠A, b is the side opposite to the angle m∠B and c is the side opposite to the angle m∠C.

sine of the angle scan be found using calculator.

From the question,

1) In first triangle side,

AB = 12ft, BC = 17 ft and m∠A=26°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 26°/17 = sin B/AC = sin C/12

sin 26°/17 = sin C/12

12×sin 26° = 17×sin C

sin C = 5.26/17 = 0.3091

C = 18.023° ≈ 18°

3) In second triangle side,

m∠B = 27°, AB = 19 in and m∠A = 115°

m∠A + m∠B +m∠C = 180°

115° + 27° + m∠C = 180°

142° + m∠C = 180°

m∠C = 38°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 115°/BC = sin 27°/AC = sin 38°/19

sin 27°/AC = sin 38°/19

sin 27° × 19 = sin 38° × AC

8.63 = 0.62 × AC

AC = 13.91 in ≈ 14 in.

Hence in first triangle side angle m∠C is 18° and in first triangle side AC is 14 in.

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Answer:

F+V=E+2

F=6

V=8

E=?

PUT THEIR VALUE

6+8=E+2

= 14=E+2

=14-2=E

=12=E

VALUE OF E IS 12

Since the jet bomber arrived over its Target at the same time as its fighter jet escorted, it took the jet bomber 0.34 h to reach the target.

To find the number of hours, we need to solve simultaneous equations.

Simultaneous equations are pair of equations which contain two unknowns.

Let

So, D = vt

D = 500t  (1)

Also, D = VT

D = 60T  (2)

Since  jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off.

T = t + 2.5

So, D = 60(t + 2.5)  (3)

D = 500t  (1)

D = 60(t + 2.5)  (3)

Equating equations (1) and (3), we have

500t = 60(t + 2.5)

500t = 60t + 150

500t - 60t = 150

440t = 150

t = 150/440

t = 15/44

t = 0.34 h

So, it took the jet bomber 0.34 hours to reach the target.

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Answer: 7(8x + 6) = -1: Exact form: x = -43/56, decimal form: x = -0.76785714

Thats all i have because you can't solve for x for the second one!

Answer:

24 combinations

Step-by-step explanation:

To get to this answer, I multiplied 6 x 4, since there are 6 shirts and 4 pairs of jeans, there will be a total of 24 combinations. For combinations of two different things, you can just multiply the amount of each item by the other item. hope this helps :)

The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

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Answer:

11.281

Step-by-step explanation:

For this question, since we see a right angle triangle, we know that we can use Pythagoras' Theorem to solve for this question.

By Pythagoras' Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {4.6}^{2} + {10.3}^{2} \\ \\ {x}^{2} = 127.25 \\ x = \sqrt{127.25} \\ = 11.281 \: or \: \frac{ \sqrt{509} }{2} [/tex]

The transformation of the coordinate (-8, -3)  R 270° and T-2,-1 is (-5, -9)

Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.

Analysis:

When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)

so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)

When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9

Therefore the transformed coordinate becomes (-5, -9)

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Answer: Right isosceles triangle

Step-by-step explanation: This is fairly easy to determine.

Side BC is roughly congruent to side CD. Both sides start from 0 to 7 and a little bit.

Side AC is also congruent by the reflexive property and is also congruent to both triangles' sides because it lines up perfectly. Since both sides BC and CD are congruent, the segment AC likely is perpendicular to segment BD and cuts it into 2 equal and congruent sides.

Sides AB and AD cannot be determined to be congruent.

Since the right angles are between two congruent sides of two triangles, the two triangles are congruent by the Side Angle Side congruence theorem.

Thus, we can say these are 2 right isosceles triangles conjoined together. Hope this helped!

(Proof is attached.)

18% of the milk mixture and how much of the cream mixture should he use.

A dairyman wants to combine milk with 5 percent butterfat and cream with 75 percent butterfat to create a 56-liter combination. Butterfat should make up 53% of the final combination.

Let x represent the volume of MILK required for the combination, in liters.

Consequently, x/56 is the PROPORTION of milk in the mixture. [because the final mixture has 56 liters in total]

We require 56 - x liters of CREAM in the mixture because we have 56 liters overall in the mixture.

The PROPORTION of cream in the combination is therefore equal to (56 - x)/56.

Our goal is for the final mixture to have 75% butterfat.

Fill in the equation with each of these values to obtain:

50 = (x/60)(5) + ((60 - x)/60) (75)

Add 56 to both sides to get: 3000 = (5)(x) + (56 - x)(75)

The formula is:

Multiply both sides by 56 to get: 3000 = (5)(x) + (56 - x)(75)

Expand: 3000 = 5x + 4200 - 75x

Simplify: 3000 = 4200 - 70x

Subtract 4500 from both sides: -1300 = -70x

Solve: x = (-1300)/(-70) = (1300)/(70) = 130/7

If you don't want to divide 130 by 7, you can evaluate this quickly by first realizing that 30/7 = 18.

Consequently, 130/7 must be a little larger than 18.

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Answer:

[tex]\frac{1}{7w^{2} }[/tex]

Step-by-step explanation:

The expression can be simplified only if you take the same quantity out of both the top and bottom.

You can simplify the numbers by taking a factor of 3 out of the expression.

The numerator changes to 1 (because 3 / 3 = 1) and the denominator changes to 7 (because 21 / 3 = 7).

The variables can be eliminated through subtraction. The numerator variable is completely removed because you can subtract w³ from w⁵. This makes the denominator w² (because w⁵ - w³ = w²).

after 6.2 hours the dose will decay to 70% in your bloodstream.

We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:

[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]

If the dosage needs to decay to a 70% of the initial dosage, then we must have:

[tex]e^{-t*ln(2)/12h} = 0.7[/tex]

Now we need to solve that for t:

If we apply the natural logarithm in both sides, we get:

[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]

So after 6.2 hours the dose will decay to 70% in your bloodstream.

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The total number of 5 digit palindrome that we have is 900.

This is the term that is used to refer to a number or a word phrase that is the same way when it is written from the front and from the back.

Examples of palindrome numbers are

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La solución de la ecuación de valores absolutos es x = - 1 y la solución de la inecuación de valores absolutos es x ≥ 9/2 ∨ x ≤ 3.

En esta pregunta debemos resolver una ecuación de valores absolutos y una inecuación de valores absolutos, cuya resolución requiere la aplicación de la definición de valor absoluto y procedimientos algebraicos:

|3 x - 1| = |3 · x + 7|

[tex]\left|\frac{3\cdot x - 1}{3\cdot x + 7} \right| = 1[/tex]

Por definición de valor absoluto:

[tex]\frac{3\cdot x - 1}{3\cdot x + 7} = 1\,\lor\,-\frac{3\cdot x - 1}{3\cdot x + 7} = 1[/tex]

[tex]3\cdot x - 1 = 3\cdot x + 7\,\lor \,- 3\cdot x + 1 = 3\cdot x + 7[/tex]

[tex]NaN \,\lor \, 6\cdot x = -6[/tex]

x = - 1

|4 · x + 3| ≤ 15

Por definición de valor absoluto:

- 4 · x + 3 ≥ - 15 ∨ 4 · x + 3 ≤ 15

- 4 · x ≥ - 18 ∨ 4 · x ≤ 12

x ≥ 9/2 ∨ x ≤ 3

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Answer: the maximum is (-2,5 )and the equation for the axis of symmetry is  x = -2

Explanation if you want:

for the min and max:  when a quadratic has a maximum point, that is the largest point that it will ever be at.  When it has a minimum, that is the smallest.

for the axis of symmetry: basically, this is the line that splits the graph into two equal parts.

there u go

Answer: a, c, e

Step-by-step explanation:

a) True. If x=0, f(0)=c.

b) False. Considering the quadratic formula, we know the solutions are not always x=c.

c) True. This is a standard fact.

d) False. If the discriminant is not positive, there are less than two x-intercepts.

e) True. If you plug into the formula [tex]x=-\frac{b}{2a}[/tex], if b=0, then obviously the x-coordinate of the vertex is also 0.

Due to its subject-specific classification, ink color in pens is a qualitative variable.

Consequently, option (C) is the appropriate choice.

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