The graph of the function f(x) = (x + 2)(x − 4) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0). Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0

Answer:

an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle (since the sign is "left than")

Step-by-step explanation:

Given the inequalities

17+4x < 9

Subtract 17 from both sides

17+4x -19 < 9 - 17

4x < -8

Divide both sides by 4

4x/4 < -8/4

x < -2

To represent the solution on a number line, an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle.

Answer:

[tex] \frac{1}{ {6}^{8} } [/tex]

Step-by-step explanation:

when the is a base raised to a negative power.....put it under 1 and the negative power now becomes a positive power

Example: 5^-2 = 1/5^2

Answer:

C

Step-by-step explanation:

Complete Question:

A circle is shown. Chords A C and B D intersect at point E. The length of A E is x, the length of E C is x + 12, the length of B E is x + 2, and the length of E D is x + 5. BE is 2 units longer than AE, DE is 5 units longer than AE, and CE is 12 units longer than AE. What is BD?

*The circle is attached below in the attachment

Answer:

BD = 11

Step-by-step explanation:

Given:

AE = x

EC = x + 12

BE = x + 2

ED = x + 5

Required:

Length of BD

Solution:

First, create an equation to find the value of (x + 2)(x + 5) = (x)(x + 12) => intersecting chords theorem

x(x + 5) + 2(x + 5) = x(x + 12)

x² + 5x + 2x + 10 = x² + 12x

Add like terms

x² + 7x + 10 = x² + 12x

Subtract x² from each side

x² + 7x + 10 - x² = x² + 12x - x²

7x + 10 = 12x

10 = 12x - 7x

10 = 5x

10/5 = 5x/5

2 = x

x = 2

Next, find BD:

BD = BE + ED

BD = x + 2 + x + 5

Add like terms

BD = 2x + 7

Plug in the value of x

BD = 2(2) + 7

BD = 4 + 7

BD = 11

Answer:

What is BD?

11  units

Step-by-step explanation:

Answer:

56851200

Step-by-step explanation:

The expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12

A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56 etc. are the numbers.

It is given that:

The word expression:

"five thousand six hundred eighty-five and twelve hundredths"

The number would be:

= 5685.12

In the expanded form the number can be written as:

The expanding form can be used to indicate the value of each digit in a number in arithmetic.

Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.

Expanded Form:

5685.12 = 5000 + 600+ 80 + 5 + 0.1 + 0.02

Thus, the expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12

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Answer:

1000

Step-by-step explanation:

the math

Answer:

3.75

Step-by-step explanation:

r²+9²=(6+r) ²

r²+81 = 36+12r + r²

81=36+12r

=> 12r = 45

r = 45/12 = 3.75

Answer:

The distance is 12 miles

Step-by-step explanation:

Given

See attachment for grid

Required

The distance

From the attached:

[tex]B = (-8,6)[/tex] --- Bank

[tex]H = (4,6)[/tex] --- Hiroto's house

Using distance formula, we have:

[tex]d = \sqrt{(x_1- x_2)^2 + (y_1 - y_2)^2}[/tex]

This gives:

[tex]d = \sqrt{(-8- 4)^2 + (6 - 6)^2}[/tex]

[tex]d = \sqrt{(-12)^2}[/tex]

[tex]d = \sqrt{144}[/tex]

[tex]d = 12[/tex]

Answer:

-3x+30

Step-by-step explanation:

[tex]4\left(x+7\right)-7x+2[/tex]

Expand [tex]4(x+7)= 4x+28[/tex]

[tex]4x+28-7x+2[/tex]

Simplify [tex]4x+28-7x+2[/tex]

[tex]-3x+30[/tex]

Answer:

11.8 ft

Step-by-step explanation:

Since the length of one side, l = 5.3 ft, the longer base b = 12.7 ft and the one brace, d form a triangle with angle between the longer base and side being the angle facing the brace is θ = 68.4°, we use the cosine rule to find the length of thee brace.

So d² = l² + b² -2lbcosθ

So, substituting the values of the variables into the equation, we have

d² = (5.3 ft)² + (12.7 ft)² -2(5.3)(12.7)cos68.4°

d² = 28.09 ft² + 161.29 ft² - 134.62(0.3681)

d² = 189.38 ft² - 49.56 ft²

d² = 139.82 ft²

taking square-root of both sides, we have

d = √139.82 ft²

d = 11.82 ft

d ≅ 11.8 ft to the nearest tenth of a foot.

Answer:

675 sq feet

Step-by-step explanation:

Radius =15ft

Area = 3(15)^2

= 3(15)(15)

= 3(225)

=675 sq ft

Answer:

675

Step-by-step explanation:

We square r first, so 15 ^ 2 = 225.

Then multiply by pi, which is 3 for this problem. 225 x 3 = 675.

Therefore, the answer is 675.

Answer: [tex]AB=CD=13\ cm\ \text{and}\ BC=AD=35\ cm[/tex]

Step-by-step explanation:

Given

ABCD is a parallelogram

Side AD is 9 cm more than twice AB i.e.

[tex]AD=9+2AB[/tex]

Also, for parallelogram

[tex]\Rightarrow AB=CD,BC=CD[/tex]

Perimeter is the sum of the sides

[tex]\therefore AB+BC+CD+AD=96\\\Rightarrow AB+AD+AB+AD=96\\\Rightarrow AB+AD=48\\\\\text{Substitute the value of AD}\\\Rightarrow AB+9+2AB=48\\\Rightarrow 3AB=39\\\Rightarrow AB=13[/tex]

So, [tex]AD=35\ cm[/tex]

Thus, [tex]AB=CD=13\ cm\ \text{and}\ BC=AD=35\ cm[/tex]

Answer: AB=11

AD=31

BC=31

CD=11

Step-by-step explanation:

Answer:

18.84 feet.

Step-by-step explanation:

The formula for the circumference of a circle is:

2Pi*radius

The radius would be half the diameter so 3.

2*3.14*3

Answer:

QSR = 68º

Step-by-step explanation:

TSQ + QSR = TSR

15x + (10x - 2) = 173

Combine like terms

25x = 175

Divide both sides by 25

x = 7

QSR = 10x - 2

QSR = 10(7) - 2

QSR = 68º

Answer:

104

Step-by-step explanation:

18 for the bottom section, 35 for the middle section, and 51 for the top triangle.

Answer:

A

Step-by-step explanation:

If lines are parallel and intersected by another line then there are 2 alternating angles between them.

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {c) \:1}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] = \frac{1}{9} \times 9\\[/tex]

[tex] = \frac{9}{9} \\[/tex]

[tex] = \frac{1}{1} \\[/tex]

[tex] = 1\\[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:

less than is the correct answer

Answer:

The tenths place.

Step-by-step explanation:

If you want to buy 2 1/2 lb of cheese, you want to buy 2.5lbs. The tenths place is the first place after the decimal, and the place the scale needs to show to show you 2.5lbs.

Answer:

tenths place

Step-by-step explanation:

Answer: there are 2 terms

Step-by-step explanation: A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. ... Examples of single terms: 3x is a single term.

2 terms

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. The number in front of a term is called a coefficient.

Answer:

That's a parabola

explanation:

Answer:

The size of your deposit should be $13,023.92.

Step-by-step explanation:

First, the real interest has to be calculated using the following formula:

r = [(1 + i) / (1 + inf)] - 1 ..................... (1)

Where;

i = market interest rate = Interest rate on the account = 12%, or 0.12

r = real interest rate = ?

inf = inflation rate = 10%, or 0.10

Substituting the values into equation (1) and solve for r, we have:

r = [(1 + 0.12) / (1 + 0.10)] - 1 = 0.0181818181818183

Since you will need to pay ksh144,000 at beginning of first in a 4- year program, this implies that the relevant to use in calculating the size of the deposit is the formula for calculating the Future Value (FV) of an Annuity Due as follows:

FV = P * (((1 + r)^n - 1) / r) * (1 + r) ................................. (2)

Where,

FV = Future value or the amount needed to pay on the 20th birthday = ksh144,000

P = Fixed annual payment or size of the deposit = ?

r = real interest rate = 0.0181818181818183

n = number of years = 20 - 10 = 10 (Since you will make a deposit 1 year from today annually and continue to make an identical deposit each year up to and including the year you begin college.)

Substituting the values into equation (2) and solve for P, we have:

144,000 = P * (((1 + 0.0181818181818183)^10 - 1) / 0.0181818181818183) * (1 + 0.0181818181818183)

144,000 = P * 10.8591414092614 * 1.0181818181818183

144,000 = P * 11.0565803439752

P = 144,000 / 11.0565803439752

P = $ 13,023.92

Therefore, the size of your deposit should be $13,023.92.

Here, if you use the law of sines, you cannot find the measure of the required angle. But if you use the law of cosines, you will get the desired result.

The measure of the angle C of the given triangle is 43.61°

According to the law of cosine, the square of any one side of a triangle is equal to the difference between the squares of the other two sides and double the product of the other sides and cosine angle added together between them. If AB, BC, and CA are lengths of the three sides of a triangle, then using the law of cosine, we can write

AB² = BC² + CA² - 2(BC)(CA)cos C.

Here, AB = 16, BC = 22, and AC = 21.

Now, 16² = 22² + 21² - 2 * 22 * 21 * cos C

i.e. 256 = 484 + 441 - 924 * cos C

i.e. 256 - 925 = - 924 * cos C

i.e. - 669 = - 924 * cos C

i.e. cos C = 669/924 = 0.724

i.e. C = cos⁻¹(0.724) = 43.61

Therefore the measure of the angle C of the given triangle is 43.61°

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Answer:

Equation: 4x+1+75=180

X= 26

105°

Step-by-step explanation:

When added, the two angles would create a flat angle of 180°, so just add the two angles:

4x+1+75=180

4x+76=180

   -76   -76

4x=104

x=26

Input the solved x value into the angle to get the angle measure

4(26)+1 = 105

Answer:

Following are the response to the given question:

Step-by-step explanation:

Move b a bit further if the angle between cd and ab changes when you move b if you want to make a perpendicular point to cd The angle BEC is 90 ° for making the AB line perpendicular to the line CD to transfer point B to the angle between the two lines.

Answer:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression.  

Step-by-step explanation:

(S=D/T)S=216KM, T=8HOURS : 216/8=27KM/HOUR

The average speed of the train is 27 km/hour if It takes a train 8 hours to travel a distance of 216 km.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

It takes a train 8 hours to travel a distance of 216 km.

As we know,

Average speed = distance/time

Average speed = 216/8 = 27 km/hour

Thus, the average speed of the train is 27 km/hour if It takes a train 8 hours to travel a distance of 216 km.

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Answer:

[tex]\small \sf \frac{2}{3} = x \\ [/tex]

Step-by-step explanation:

Solve for x;

2x - ( x - 2 ) = 4x

distribute minus sign through parantheses

combine like terms

subtract x from both side

Divide each side by 3

[tex] \small \sf \frac{2}{3} = \frac{3x}{3} \\ [/tex]

[tex]\small \sf \frac{2}{3} = x\: \\ [/tex]

Answer:

128 cm²

Step-by-step explanation:

Given linear scale factor of 2 similar shapes = a : b , then

ratio of areas = a² : b²

Here linear scale factor = 3 : 4 , then

ratio of areas = 3² : 4² = 9 : 16

let x be the area of the larger shape then by proportion

[tex]\frac{9}{72}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )

9x = 1152 ( divide both sides by 9 )

x = 128

That is area of larger shape is 128 cm²