f function g has the factors (x − 7) and (x + 6), what are the zeros of function g?

A.
-7 and 6
B.
-6 and 7
C.
6 and 7
D.
-7 and -6

Answer:

6 weeks :)

Step-by-step explanation:

it will take her 6 weeks

45-15 is 30.

30/5 is 6

Answer:

It will take her 6 weeks.

Step-by-step explanation:

$45-$15=$30

$30 ÷ $5 = 6

Answer:

2 and 3

Step-by-step explanation:

20/12 = 1.6666666

15/9 = 1.6666666

Among the provided vectors, only Vector 3 has equal-magnitude components.

To determine which vector has equal-magnitude components, we need to calculate the x-component and y-component of each vector.

Let's calculate the x-component and y-component of each vector:

Vector 1:

- x-component = 7 units * cos(70°) ≈ 2.39 units

- y-component = 7 units * sin(70°) ≈ 6.56 units

Vector 2:

- x-component = 5 units * cos(155°) ≈ -3.96 units

- y-component = 5 units * sin(155°) ≈ -4.72 units

Vector 3:

- x-component = 3 units * cos(225°) ≈ -2.12 units

- y-component = 3 units * sin(225°) ≈ -2.12 units

Now, let's compare the x-components and y-components of the vectors:

Vector 1 does not have equal-magnitude components since the x-component (2.39 units) is not equal to the y-component (6.56 units).

Vector 2 does not have equal-magnitude components since the x-component (-3.96 units) is not equal to the y-component (-4.72 units).

Vector 3 has equal-magnitude components since the x-component (-2.12 units) is equal to the y-component (-2.12 units).

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ANSWER:

A. 337.5 miles

STEP-BY-STEP EXPLANATION:

What we must do is calculate the distance in each section, when the speed and time vary, the sum of both section is the total distance:

Section 1:

Section 2:

The total distance is:

Answer:

160in³

Step-by-step explanation:

V = lwh

V = 5(4)(8)

V = 40(4)

V = 160in³

Answer:

b

Step-by-step explanation:

To stretch a spring 1 ft. from its natural length, a 15 ft-lb work is needed. To stretch a spring 6 in. from its natural length, the required work is 3.75 ft-lb

The work done on a spring is given by the formula:

W = 1/2 . kx²

Where:

k = spring constant

x = spring displacement

From the formula, we know that the work is directly proportional to the square of displacement, or mathematically:

                W ∝ x²

Therefore,

W₁ : W₂ = x₁² : x₂²

Data from the problem

W₁ = 15 ft-lb

x₁ = 1 ft

x₂ = 6 in. = 0.5 ft

Hence,

15 : W₂ = 1² : 0.5²

W₂ = 0.25 x 15 = 3.75 ft-lb

Hence, the required work to stretch the spring 6 in beyond its natural length is 3.75 ft-lb

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Answer:

6x^2 + 3x + 1

Step-by-step explanation:

( 5x^2 + 8x ) + ( x^2 - 5x + 1 )

= 5x^2 + x^2 + 8x - 5x + 1

= 6x^2 + 3x + 1

The square of a binomial, the value of the constant \(c\) should be equal to half the coefficient of the linear term squared, which in this case is \(c = \left(\frac{22}{2}\right)^2 = 121\). Therefore, the constant that needs to be filled in is 121.

To express the quadratic expression \(x^2 + 22x + c\) as the square of a binomial, we need to find a binomial of the form \((x + a)^2\) that expands to \(x^2 + 22x + c\). Expanding \((x + a)^2\) gives \(x^2 + 2ax + a^2\). Comparing the coefficients of the expanded binomial and the given quadratic expression, we can equate the linear terms to find \(2ax = 22x\), which gives \(a = 11\). Substituting this value of \(a\) back into the expanded binomial, we have \(x^2 + 22x + 121\). Therefore, the constant that needs to be filled in is 121.

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Answer:

YZ = 25.40 correct to 1dp

Step-by-Step explanation:

Sin16°= XZ/YZ

YZ=XZ/sin16°

YZ=7/0.276

YZ=25.3623188405797

YZ = 25.40 correct to 1dp

Answer:

XZ ≈ 24.39

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan16° = \(\frac{opposite}{adjacent}\) = \(\frac{XZ}{YZ}\) = \(\frac{7}{YZ}\) ( multiply both sides by YZ )

YZ × tan16° = 7

YZ × 0.287 = 7 ( divide both sides by 0.287 )

YZ = \(\frac{7}{0.287}\) ≈ 24.39 ( to 2 dec. places )

Answer: 50

Step-by-step explanation:

\(h\:\circ \:g=h\left(g\left(x\right)\right)\)

\(g\left(x\right)=4x-2\)

\(=h\left(4x-2\right)\)

\(=5\left(4x-2\right)\)

\(=20x-10\)

Substitute 3 for x:

= 20(3)-10

= 50

The Johnston index of each voter is 3.317 and the Deegan-Packel index of each voter is  0.154

The Johnston index and the Deegan-Packel index are two measures of voting power that take into account the number of votes each voter has and the number of votes required for passage.

a) The Johnston index is calculated by taking the square root of the product of the number of votes a voter has and the number of votes they need for passage. In this case, the Johnston index for each voter is:
MA: √(4*(12-4)) = √32 = 5.657
ME: √(3*(12-3)) = √27 = 5.196
NH: √(2*(12-2)) = √20 = 4.472
CT: √(4*(12-4)) = √32 = 5.657
RI: √(3*(12-3)) = √27 = 5.196
VT: √(1*(12-1)) = √11 = 3.317

b) The Deegan-Packel index is calculated by taking the number of winning coalitions that a voter is a part of and dividing it by the total number of winning coalitions. In this case, the Deegan-Packel index for each voter is:
MA: 20/26 = 0.769
ME: 14/26 = 0.538
NH: 8/26 = 0.308
CT: 20/26 = 0.769
RI: 14/26 = 0.538
VT: 4/26 = 0.154

Overall, the Johnston index and the Deegan-Packel index provide different perspectives on the voting power of each voter. The Johnston index takes into account the number of votes each voter has and the number of votes required for passage, while the Deegan-Packel index takes into account the number of winning coalitions each voter is a part of.

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The probability that the blood sample mixture will test positive is 0.50.

For the stated question-

The likelihood that one sample will be negative is unrelated to the likelihood that the other samples will also be negative.

The chance of the 6 combined events, all of which are negative, is then equal as the product of a probabilities for every sample (each negative).

One sample being negative has a chance of 0.89 (1 - 0.11).

The total probability is hence (0.89)⁶ = 0.497  ≈ 0.50

Thus, the probability that the blood sample mixture will test positive is 0.50.

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I am pretty sure the answer would be (2,3)

Answer:

9a³b³

Step-by-step explanation:

9a³b³(ab - 3) = 9a^4b^4 - 27a^3b^3

Answer:

9a^3 b^3

Step-by-step explanation:

GCF=Greatest common factor

jxjxjxnxnxnnxnnxncncncxxnx

Skzkkxkxkfnzxnxnncnvnvnnv XMMMXMidjjcnfnndnmcmcmcmcmcmxmdnndjd

Numerical length of VX = 20

Given

VX is a line segment which has a point W on it.

We are also given the following dimensions:

VX = 4X

VW = 3X

WX = 5

Numerical length VX :

VX = VW + WX

Substitute the values,

4X = 3X + 5

X = 5

Numerical length of VX = 4x

= 4 *5

VX = 20

Thus the length of bar VX is 20  .

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1. The measurements in fluid ounces and gallons to complete the table will be:

1 = 128

5 = 640

3 = 384

15 = 1920

2. There is a proportional relationship between a measurement in fluid ounces and a measurement in gallons for the same volume. This is because they've a constant of 128.

From the information, the relationship between a volume in fluid ounces (z) and the same volume in gallons (g) is described by the equation z=128g.

Therefore, 1 ounce = 128g

5 ounces will be:

= 5 × 128g

= 640g

384g to ounces will be:

= 384 / 128

= 3 ounces

1920g to ounces will be:

= 1920 / 128

= 15 ounces

In this case, the equation given is z = 128g. This illustrates that the constant of proportionality is 128.

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The probability that at least one of the 10 shovels purchased by CBC facility services is defective is approximately 0.4272 or 42.72%.

To find the probability that at least one of the 10 shovels purchased by CBC facility services is defective, we can use the concept of complementary probability. The probability that none of the 10 shovels is defective is equal to the probability that all of the shovels are non-defective. The probability of selecting a non-defective shovel from the batch is given by:

P(non-defective shovel) = (total number of non-defective shovels) / (total number of shovels)

In this case, there are 250 shovels in total, and out of those, 15 are defective. Therefore, the number of non-defective shovels is 250 - 15 = 235. So, the probability of selecting a non-defective shovel is:

P(non-defective shovel) = 235 / 250

= 0.94

Now, the probability of selecting all 10 shovels to be non-defective is:

P(all 10 shovels non-defective) = (P(non-defective shovel))¹⁰

= 0.94¹⁰

≈ 0.5728

Finally, to find the probability that at least one of the 10 shovels is defective, we can subtract the probability of none of them being defective from 1:

P(at least one defective shovel) = 1 - P(all 10 shovels non-defective)

= 1 - 0.5728

≈ 0.4272

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Answer: 5

1  x 5 = 5

2 x 5 = 10

The value of x = -1 and y = -2 by solving the system of equation by using the substitution are 9x - y + 7 = 0 and 13x - 4y + 5 = 0

Given that,

The system of equation are 9x - y + 7 = 0 and 13x - 4y + 5 = 0

We have to solve the system of equation by using the substitution method.

We know that,

Take the system of equation

9x - y + 7 = 0 --------->equation(1)

13x - 4y + 5 = 0  ---------> equation(2)

From the equation (1)
9x - y + 7 = 0

y = 9x + 7

Substitute y = 9x + 7 in equation(2)

13x - 4y + 5 = 0

13x - 4(9x + 7) + 5 = 0

13x - 36x - 28 + 5 = 0

- 23x - 23 = 0

-23x = 23

x = -1

Now, Substitute x = -1 in equation(1)
y = 9(-1) + 7

y = -9 + 7

y = -2

Therefore, The value of x=-1 and y=-2

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Answer:

The first one

y=1.3y+10

Step-by-step explanation:

Just test every solution,

Answer:

Step-by-step explanation:

The figure has 5 sides. Therefore the formula to solve it is (n - 2)*180

(5 - 2)*180 = 3*180 = 540

That is the total of the interior angles so

x + 86 + 140 + 138 + 59 = 540

x + 423 = 540                            Subtract 423 from both sides

x = 540 - 423

x = 117

Answer:

Answer:d

Step-by-step explanation:

The  equation relates the distance and time with a constant speed of 4 meters per second is d= 4t.

In mathematics, an equation is a statement of equality between two mathematical expressions, which are separated by an equals sign (=) and consist of variables and constants.

Di runs at a rate of 4 meters per second.

So, The equation that models the situation is:

d = 4t

where d is the distance traveled in meters, and t is the time spent running in seconds.

This equation relates the distance and time with a constant speed of 4 meters per second.

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Answer

Step by step explanation

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Answer:

answer to the question

graph

The coefficient of the product of (-5 x y²) and (-4 x²y) exists 20 .

The exponent of x in the product exists 3, and the exponent of y exists 3.

A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. Mn denoted that m has been multiplied by itself n times if m exists a positive number and n exists its exponent.

We exists to determine the product of (-5 x y²) and (-4 x² y)

The product of (-5 xy²) and (-4 x²y) can be defined as shown below

-5xy² × -4x² y

simplifying the above equation, we get

-5 × -4 × x ×  x² × y² × y

⇒ 20 × x³ × y³  

⇒ 20 x³  y³

The product of the given expressions is 20 x³ y³

Therefore, the coefficient of the product is 20.

The exponent of x in the product exists 3 and the exponent of y exists 3.

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Linear equation is the equation in which the power of the unknown variable is 1. The number of bracelet with blue beads is 10 and bracelet with red beads is 17

Given information-

Each bracelet with blue beads sells for $4. 50.

Each bracelet with red beads sells for $5.

Sarabeth raised a total of $130 for the library.

Linear equation is the equation in which the power of the unknown variable is 1

The number of bracelet with blue beads is \(b\) and the number of bracelet with red beads is \(r\).

As the number of bracelets with red beads (r) that Sarabeth sold is 3 less than twice the number of bracelets with blue beads (b) sold. Thus,

\(r=2b-3\)

Each bracelet with blue beads sells for $4. 50 and each bracelet with red beads sells for $5. Sarabeth raised a total of $130 for the library. Thus

\(130=4.5b+5r\)

Put the value of \(r\) in the above equation,

\(\begin{aligned}130 &=4.5b+5(2b-3)\\130 &=4.5b +10b-15\\130+15 &=14.5b\\b&=\dfrac{145}{14.5} \\b&=10\\\end\)

Therefore the number of blue bracelet are 10. Thus the red bracelets are,

\(r=2\times10-3\)

\(r=17\)

Hence the number of bracelet with blue beads is 10 and bracelet with red beads is 17.

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