Predict what are the real roots of the polynomial equation (x2 - 4)(x + 3)²(X -- 1 = 0.
A. +2, -3,1
B. -3,1
C. 4, 3.-1
D. 3, -110​

Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)

\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)

\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)

\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.

Answer:

4x - 3 - 2x + 5 = 6 - 3x + 2 + 5x

2x + 2 = 2x + 8

2 ≠ 8, so this equation has no solutions.

Answer:

No solution

Step-by-step explanation:

Given:

\(4x-3-2x+5=6-3x+2+5x\)

rearrange terms so like terms are together

\(4x-2x-3+5=6+2-3x+5x\)

combine like terms

\(2x+2=8+2x\)

subtract 2x to both sides

\(2\neq 8\)

2 doesn't equal 8, meaning that there are 0 solutions to this problem.

Hope this helps! :)

Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

The graph of the linear function 4x + 6y = -12 is given by the image presented at the end of the answer.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The function for this problem is given as follows:

4x + 6y = -12.

In slope-intercept form, the function is given as follows:

6y = -4x - 12.

y = -2x/3 - 2.

The slope and the intercept are given as follows:

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Answer:

D)12.5

Step-by-step explanation:

y/2.5=5

y=5*2.5

y=12.5

Answer:

3

Step-by-step explanation:

Since there are 12 papers and 4 piles, we do 12/4=3 so 3 papers in each pile.

Answer:

this one has to be answer 1

Step-by-step explanation:

4x - y = -5

x + 2y =1

8x - 2y = -10

x + 2y = 1

9x = -9

The quadratic function that represents the given graph is:

y = ¹/₂(x − 4)² - 1

The general form of a quadratic equation in Vertex Form is expressed as:

y = a(x − h)² + k,

where

(h, k) is the vertex.

From the given graph, we can see that the coordinates of the vertex is (4, -1). Thus, we have:

y = a(x − 4)² - 1

Looking at the four given options from Option A to Option D, we can deduce that only given option that gives us the coordinates of the quadratic curve vertex is option D.

Thus, we can conclude that the quadratic function that truly represents the given parabolic graph curve is:

y = ¹/₂(x − 4)² - 1

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From the remainder theorem, the remainder will be -2 and the relationship between f(x) and x + 2 is an inverse relationship.

The remainder theorem is used to determine the remainder where a polynomial is divided by a binomial.

The remainder theorem states that if a polynomial p(x) is divided by a binomial x - a, the remainder of the division is p(a).

Given the following division, f(x)/ x + 2

We can rewrite the binomial in this form:

x + 2 = x - (-2)

The division then becomes:

f(x)/ x - (-2)

From the remainder theorem, the remainder will be -2.

Therefore, the relationship between f(x) and x + 2 is an inverse relationship such that f(2) = -2

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Answer:

\(z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557\)

And using the normal standard distribution and the complement rule we got:

\(P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06\)

Step-by-step explanation:

For this case we define our random variable X as "fat content per hot dog" and we know the following parameters:

\(\mu = 20, \sigma =1.9\)

We select a sample of n=35 and we want to find the following probability:

\( P(\bar X>20.5)\)

For this case since the sample size is >30 we can use the central limit theorem and we use the z score formula given by:

\(z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}\)

Replacing we got:

\(z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557\)

And using the normal standard distribution and the complement rule we got:

\(P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06\)

Answer:

A = 18

B = 88

C = 74

Step-by-step explanation:

Givens

B = 3*A + 34

C = A + 56

Equation

A + B + C = 180

Solution

A + 3A + 34 + A +56 = 180   Collect like terms

5A + 90 = 180                  Subtract 90 from both sides

5A = 180 - 90

5A = 90                            Divide by 4

A = 90 / 5

A = 18

Answer

B = 18*3 + 34 = 54 + 34 = 88

C = 74

Check

A + B + C = 18 + 88 + 74

A + B + C = 180 as it should.

Answer:

(1/2) x (5/6) = 5/12

Step-by-step explanation:

Just multiply those fractions together.

(1/2) x (5/6) = 5/12

Answer:

Step-by-step explanation:

Angelica started her journey with half a tank of gas, equivalent to x/2. She used x/4 for half the distance, meaning she only covered half the distance of a full tank. She needs three full tanks for her destination, so she will have to stop for refills three times.

Step-by-step explanation:

Answer:

Answer:2

Step-by-step explanation:

You use the slope equation so -11 -(-1) would be -11+1 because the negatives cancel each other out and you get -10. Then 4-9 is -5 and then -10 divided by -5 is a positive 2.

Step-by-step explanation:

Domain = set of input value

Range = set of output values

The length of the rectangle is 48 yards.

Let's denote the width of the rectangle as "w" yards.

According to the information given, the length of the rectangle is 32 yards less than 10 times its width. So, the length can be represented as: 10w - 32 yards.

The formula for the area of a rectangle is length times width: Area = length × width.

Given that the area of the rectangle is 384 square yards, we can set up an equation:

Area = length × width

384 = (10w - 32) × w

Now, let's solve for the width (w):

384 = 10w² - 32w

0 = 10w² - 32w - 384

Dividing the equation by 2 to simplify:

0 = 5w² - 16w - 192

Now we have a quadratic equation. We can either factor it or use the quadratic formula to solve for "w." Let's use the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

For our equation, a = 5, b = -16, and c = -192. Plugging these values into the formula:

w = (16 ± √((-16)² - 4 × 5 × (-192))) / (2 × 5)

w = (16 ± √(256 + 3840)) / 10

w = (16 ± √4096) / 10

w = (16 ± 64) / 10

This gives us two possible solutions for the width:

w = (16 + 64) / 10 = 8 yards

w = (16 - 64) / 10 = -4.8 yards

Since width can't be negative, we'll ignore the second solution.

So, the width of the rectangle is 8 yards. Now, let's find the length using the earlier expression:

Length = 10w - 32

Length = 10 × 8 - 32

Length = 80 - 32

Length = 48 yards

Therefore, the length of the rectangle is 48 yards.

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Answer:

68

Step-by-step explanation:21+6+6+14+21=68

Answer:

82

Step-by-step explanation:

Calculate the area of each part and sum them up

S= 7x3+7x2+7x3+2x3+2x3+7x2

42+28+12

=82

hope this helps!

Answer:

D

Step-by-step explanation:

Answer:

Giraffe = 10

Guinea Pig = 4

Tiger = 16

Step-by-step explanation:

G       GP      T                                  = 30

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

X      X-6     (X-6)*4

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

9         3         12                               = 24

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

10       4         16                               = 30 ✅

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

Answer:

12 or 16

Step-by-step explanation:

because it was a good thing for you to be here with us today so I don't have any money in my hands and you don't want me back in

\(4(x + 1) = 5(x - 3) \\ 4x + 4 = 5x - 15 \\ 5x - 4x = 4 + 15 \\ x = 19\)

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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Answer: 7

Step-by-step explanation:

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

9-6+4

=7

Given triangles ADE and ABC, you know that they are congruent.

By definition, two triangles are congruent when the measures of their corresponding angles are equal and the lengths of the corresponding sides are equal.

In this case, you can identify that:

And:

Then, knowing that:

You can determine that:

Hence, the answer is:

The required graph has been attached below that represents the function f(x) = 5 cos (2x).

The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.

Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.

The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).

Thus, the graph has been attached below that represents the given function.

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Answer:

V = 1/3 * π * r^2 * h OR V = π * r^2 * h/3

Step-by-step explanation:

hope it will help you dear

you told only formula if you need derevation then say :)