Which expression fits this description?
• The expression is the sum of two terms.
• The first term is the product of 2 and a.
• The second term is the quotient of b and 4.

A. 2a + (b-4)
B. (2+ a) + b/4
D. 2a + b/4
C. (2+a) + (b-4)

Answer:

Option 2

Step-by-step explanation:

The side lengths satisfy the Pythagorean theorem.

Answer:

3 + 1.2c>13.50

Step-by-step explanation:

Graph point in line, number  10

Answer:

the answer is 84 degrees

Step-by-step explanation: add 15 degrees to 69 degrees

Given that CD is the midsegment of the trapezoid WXYZ

From the properties of Midsegment of trapezoid we have :

0. The midsegment of a trapezoid is parallel to each base.

1. The length of the midsegment of a trapezoid is equal to half the sum of the lengths of its bases.

In the given figur, the mid segement CD= 22

length of parallel side is WZ=x+3

and the length of another side XY = 4x+1

so apply the mid segment length formula :

x=8,

For, XY :

Substitute x=8 into the given length expression of XY

XY =4x+1

XY=4(8)+1

XY=33

For, WZ :

Substitute x=8 into the given expression length of WZ

WZ=x+3

WZ=8+3

WZ=11

Answer :

a). x = 8

b). XY = 33

c). WZ = 11

Answer:

I hope this helps!

Answer:

sin(t) = √15/4,

cos(t) = - 1/4,

tan(t) = - √15

Step-by-step explanation:

The coordinates of the terminal point P(x, y) determined by t are x = - 1/4, and y = √15/4;

sin(t) = y = √15/4

cos(t) = x = - 1/4

tan(t) = y/x = √15/4 / - 1/4 = - √15

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

Step-by-step explanation:

The slope of the line is 1/2 because it goes right one, and up 2.

It can be shown the slope is constant because every time you go up 2 and to the right one, there is a point, which means that the slope will go on infinitely in that direction, with the same slope.

Answer:

y≤2x-1

Step-by-step explanation:

The sign mean less than or equal to

Given data:

A: Electricla projects

B: roofing projects

C: butget greater than $275,000

Venn diagram: B

b) The region that contains electrical projects and roofing projects with a budget greater than $275,000 is the region of intersection of sets A, B and C:

Region V, in this region all groups intersect (Elements that are in A and B and C)

c) The region that contains the roofing projects with budget greater than $275,000 (Intersection of sets B and C) that are not electrical projects (A complement or A' is the set of elements that are not in A) is:

Region VI

The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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The most likely to be discussed in a feminist criticism of Chinua Achebe's work is his portrayal of gender roles and  Ina is a typical woman . The correct option is 2.

What is a novelist person?

A novelist is a person who writes novels. The key to success as a romantic novelist is absolute belief in your story. Synonyms: author, writer More Synonyms of novelist

Who is Chinua Achebe?

Chinua Achebe is a novelist and poet. He  is famous for his pivotal direction in literature of Africa. His first novel was Things fall apart.

The options are attached here:

his life story and literary achievements

his portrayal of gender roles

his descriptions of the landscape

his literary influences and preferences

Thus, the correct option is 2. his portrayal of gender roles.

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Answer:

y/x  Jonathan age divided by Jean's age

Step-by-step explanation:

hope this helps

Jonathon is [y/x] years older than Jean.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have Jean is [x] years old and Jonathan is [y] years old

Assume that Jonathon is [m] years older than Jean. Then we can write -

y = mx

or

m = y/x

Therefore, Jonathon is [y/x] years older than Jean.

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The correct option is A) 20.2.

What is triangle sum?

The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.

Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:

Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:

K = 180 - A - B

= 180 - 84 - 65

= 31 degrees

Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:

sin(A)/x = sin(K)/17

Substitute the values we know into the equation and solve for x:

sin(84)/x = sin(31)/17

x = sin(84)*17/sin(31)

Using a calculator, we get:

x ≈ 20.2

Therefore, the value of x in the triangle is approximately 20.2.

So, the correct option is A) 20.2.

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Answer:

The bisector is line l

mq = 7

Step-by-step explanation:

To find x:

\(5x-3=11-2x\\\\+2x+3 +3 +2x\\\\\\7x=14\\x=2\)

To find the value of mq

plug in the value of x into the equation.

\(11-2x\\11-2(2)\\11-4\\=7\)

MQ = 7

Hope this is helpful! Please leave a review and comment below! Thanks for all your support!  

b. B

PM = RM

\(5x - 3 = 11 - 2x\)

\(5x + 2x = 11 + 3\)

\(7x = 14\)

\(x \times 2\)

MQ = \(11 - 2x\)

\(11 - 2 \times 2\)

\(11 - 4\)

\( = 7\)

Answer:

a). Horizontal distance = 11.1 m

b). Maximum height = 6.2 m

c). Firefighter is 13.7 m from the house

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

Height of the water can be determined by the expression,

h(x) = -0.026x²+ 0.577x + 3

Here x = Horizontal distance of the from the firefighter

a). Since the stream of the water will follow a parabolic path, maximum point of the parabola will be = Vertex of the parabolic path

Horizontal distance from the firefighter at which the water achieves the maximum height = -\(\frac{b}{2a}\)

From the quadratic function,

h(x) = -0.026x²+ 0.577x + 3

a = -0.026

b = 0.577

Therefore, the horizontal distance = \(-\frac{0.577}{2\times (-0.02612)}\) = 11.05 m

                                                         ≈ 11.1 meters

b). By putting x = 11.1 in the quadratic equation,

    h(x) = -0.02612(11.1)²+ 0.577(11.1) + 3

           = -3.2182 + 6.4047 + 3

           = 6.18 m

           ≈ 6.2 m

c). For h(x) = 6 m

    6 = -0.02612x² + 0.577(x) + 3

    0.02612x² - 0.577x + 3 = 0

    From quadratic formula,

    x = \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

    x = \(\frac{0.577\pm \sqrt{(-0.577)^2-4(0.02612)(3))}}{2(0.02612)}\)

    x = \(\frac{0.577\pm\sqrt{0.019489}}{0.05224}\)

    x = \(\frac{0.577\pm0.1396}{0.05224}\)

    x = 13.7 m, 8.37 m

Therefore, the farthest distance of the firefighter from the house will be 13.7 m

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

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

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Hope this helps! :)

Answer:

Two Portions!!!

Step-by-step explanation:

Answer:

The two possible cases are

(i) the base angles are each 40° and the vertex angle is 100°,

(ii) the base angles are each 70° and the vertex angle is 40°.

Step-by-step explanation:

Answer:

A ≈ 297.33

Step-by-step explanation:

\(radius=5\)

\(height=13\)

Using the formulas:

\(A=\pi rl+\pi r^2\)

\(l=\sqrt{r^2+h^2}\)

Solving for A:

\(A=\pi r(r+\sqrt{h^2+r^2})=\pi *5*(5+\sqrt{13^2+5^2})\) ≈ \(297.32643\)

Therefore, the surface area of the cone is 297.33.

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Answer:

$38.25

Step-by-step explanation:

45 × 0.15 = 6.75

45 - 6.75 = 38.25

The sale price of the item will be $38.25

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a store is having a sale. All items for sale are discounted by 15%. the regular price of a bedspread is $45,

The discounted price will be calculated as:-

45 × 0.15 = 6.75

45 - 6.75 = $38.25

Therefore, the sale price of the item will be $38.25

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There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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Answer:

x = 8.4

Step-by-step explanation:

take 64 degree as reference angle

using cos rule

cos 64 = adjacent / hypotenuse

0.438 = 3.7 / x

x = 3.7 / 0.438

x = 8.44

x = 8.4

The solution is, the percent of error, rounded to the nearest percent is 25%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

now, we have to find the percent of error, rounded to the nearest percent.

so, we get,

Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

so, error = 750 - 600

              = 150

so, we get,

the percent of error = 150 * 100 / 600

                                 = 25%

Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.

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-10

Step-by-step explanation:

x = 10

x2 - 2(x + 5)

10(2) - 2(10+5)

20 - 2(15)

20 - 30

-10

The value of each variable in the triangle are:

x = 28 units

y = 7√6 units

z = 14√3 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Considering the upper triangle:

cos 45° = (14√2)/x

x = (14√2)/cos 45°

x = 28 units

hypotenuse =√((14√2)² + 28²) = 14√6 units

Considering the lower triangle:

The two triangles share the same hypotenuse.

Thus, hypotenuse = 14√6 units

sin 30° = y/hypotenuse

sin 30° = y/(14√6)

y = (14√6) * sin 30°

y = 7√6 units

cos 30° = z/hypotenuse

cos 30° = z/(14√6)

z = (14√6) * cos 45°

z = 14√3 units

Therefore, the value of each variable are x = 28 units, y = 7√6 units and z = 14√3 units.

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The probability that a and b are connected, is 30%.

P(A to B) equals P(A to B open road | R5 closed). U P (road A to B open | R5 open)

errs in fact. It ought to be P. (A to B) = P(road A to B open | road 5 closed)*P (R5 closed) (R5 is open and route A to B is open) U (R5 open)

Since the two are not connected, you can use + in place of the U.

R1 and R2 are required if R5 is closed, or (both R3 and R4). Each path has a probability of being open (1p)2, but since you double-counted the likelihood that both are open, the total is 2(1p)2(1p)4, and this portion adds p(2(1p)2(1p)4) to the overall success probability.

R1 or R3 is necessary if R5 is available (R2 or R4).

= 2(1p)2(1p)4

=which is 30%

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