Divide using synthetic division (x^3 - 4x + 6) ÷ (x+3) =

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

EXPLANATION

If the measure of ∠2= x+78 and the other ∠=40 degrees, by definition we know that sum of interior angles of a triangle is equal to 180 degrees.

Furthermore, we have two congruent legs, so this is an Isosceles triangle with two congruent angles (with the same measure).

Thus,

180 = 40 + 2* m∠2

Substituting m∠2 by the equation as follows:

180 = 40 + 2(x + 78)

Subtracting -40 to both sides:

180 - 40 = 2(x+78)

Simplifying:

140 = 2(x+78)

Dividing both sides by 2:

140/2 = x + 78

Simplifying:

70 = x + 78

Subtracting -78 to both sides:

70 - 78 = x

Simplifying:

-8 = x

Switching:

x = -8

Answer: The value of x is -8.

Answer:

2

Step-by-step explanation:

40 x 5 ÷ 100

2 x 5 ÷ 5 = 2

The proper sampling technique used when the number of samples is less than 100 is saturated sampling where the entire population will be the research sample.

What is saturated sampling ?

According to Arikunto if the population is less than 100 people so the researcher need to take all the samples namely saturated sampling.

What is stratified sampling ?

Stratified sampling is a sampling technique which used when we do a research on a heterogenous population. How to use this technique is to divide the population into several stratum and then take random samples from each stratum an then all the samples that have been taken are collected into one sample.

In conclusion, if the population has fewer than 100 people , the expert suggested to use saturated sampling.

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Let's check each inequality if the value x = 5 is part of the solution:

a. x < 2

5 is a value greater than 2, so it isn't part of the solution of this inequation.

b. x > 9

5 is lesser than 9, so it isn't part of the solution of this inequation.

c. x < 18

5 is lesser than

In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).

So, the wrong step will be:

Then, the next step should be:

But, the steps it is given as:

Which makes the error.

Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).

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Answer: Location of T' on the coordinate axis will be (16,7).

T (6,4) → T' (16,7).

Step-by-step explanation:

coordinate vertices of points in rectangle JKLM are:

J (-8,-8)

K (-4,-8)

L (-4,-5)

M (-8,-5)

and coordinate vertices of points in rectangle J'K'L'M' are:

J' (2,-5)

K' (6,-5)

L' (6,-2)

M' (2,-2)

coordinate vertices of points in Quadrilateral STUV are:

S (1,4)

T (6,4)

U (4,6)

V (2,6)

transformation in coordinate vertices from rectangle JKLM to rectangle J'K'L'M' is:

J (-8,-8) → J' (2,-5)

⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.

and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.

similarly for

K (-4,-8) → K' (6,-5)

⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.

and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.

L (-4,-5) → L' (6,-2)

⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.

and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.

M (-8,-5) → M' (2,-2)

⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.

and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.

So, the location of T' of the Quadrilateral S'T'U'V' on the coordinate plane will be:

along x axis the Quadrilateral will shift towards right by 10 units

So, 6 → 6+10=16

and along y axis the Quadrilateral will shift upwards by 3 units

So, 4 → 4+3=7

⇒ T (6,4) → T' (16,7).

Step-by-step explanation:

Answer:

===========================

We know parallel lines have equal slopes, so line r has the slope of - 1.

Line r is:

Substitute the coordinates of the point into this equation and find the value of b:

The equation of line r is:

Answer:

The sum of the angles is 180°.

We already know that one angle is 90°, and the other one is 38.

so: 180-(90+38)=52°

the exterior angle+52°= 180° (beacuse the form a flat angle)

so x=180-52

so: x=128°.

Answer:

128°

Step-by-step explanation:

We know that,

   the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.

Accordingly,

38 + 90 = x

128° = x

The value of x from the given equations is 0.6.

The given equations are y=4x and y=-x+3.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, 4x=-x+3

⇒ 4x+x=3

⇒ 5x=3

⇒ x=3/5

⇒ x=0.6

Hence, the value of x from the given equations is 0.6.

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Answer:

b, d

Step-by-step explanation:

20/-4 = -5

20 x (-1/4) = -5

Answer: it would be about 1:30pm

Step-by-step explanation:

we have the expression

step 1

squared 4 before multiplying

therefore

step 1 is incorrect

Justine's work is incorrect

Answer:

h(x)

Step-by-step explanation:

y-intercept is shorthand for  ' y - axis intercept'

the graph which intercepts the y-axis the highest is   h(x)

Answer: B 10.6

Explanation:

We would assume that the stock tank is cylindrical. We would calculate the volume by applying the formula,

Volume = πr^h

where

π = 3.14

r is the radius of the cylinder

h is the height of the cylinder

From the information given,

diameter = 3

radius = diameter/2 = 3/2

r = 1.5

h = 1.5

Volume = 3.14 x 1.5^2 x 1.5 = 10.5975 cubic meters

By rounding to the nearest tenth,

Volume = 10.6 cubic meters

Let x be the number of miles the family travel in 4 days

620 miles = 2 days

x = 4 days

cross-multiply

2x = 2480

Divide both-side of the equation by 2

x = 1240 miles

Answer:45212176

Step-by-step explanation:calculator

Answer:

82x82x82x82, or 82 squared to the 4th power, is 45212176.

Answer:

[tex] \huge{ \boxed{gof(3) = 9}}[/tex]

Step-by-step explanation:

In order to find gof(3), we first have to find gof(x). To find gof(x) substitute the f(x) into g(x). That is, for every x found in g(x) substitute it by f(x).

From the question

[tex]f(x) = 2 {x}^{2} - x - 15 \\ g(x) = - 5x + 9 \\ \\ gof(x) = - 5(2 {x}^{2} - x - 15) + 9 \\ gof(x) = - {10x}^{2} + 5x + 75 + 9 \\ \\ gof(x) = - {10x}^{2} + 5x + 84[/tex]

To find gof(3), substitute the value of x that is 3 into gof(x). For every x found in gof(x), replace it by 3 and solve.

[tex]gof(3) = - 10( {3})^{2} + 5(3) + 84 \\ \quad \: \: \: \: \: = - 10(9) + 15 + 84 \\ \: \: \: = - 90 + 15 + 84 \\ = 9[/tex]

We have the final answer as

Step-by-step explanation:

fraction of page of photograph is 3/32

(1/2÷4)*3/4

1/2*1/4*3/4

1/8*3/4

=3/32

Answer:

C. C and E

Step-by-step explanation:

The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.

C and E are the solutions to this system.

Given the following question:

Natural numbers are positive integers.

5 is a natural number

Whole numbers are integers, neither fraction or decimals just integers.

5, and 0 are whole numbers

Integers are a set of numbers that can be expressed without being a fraction/decimal.

-1, 5, and 0 are integers.

Rational numbers are a set of numbers that can be written as fractions.

-1, 5, 1/2, 5/7, 0, 76/77, 1.27 are all rational numbers they can all be expressed as a fraction.

(zero is also rational)

Irrational numbers cannot be expressed as a fraction

√2, √8,

Real numbers are numbers that include rational and irrational numbers.

-1, 5, 1/2, 5/7, 0, 76/77, -1.27, √2, √8

GCF = 14

LCM = 168

let x and y be the numbers

if X = 56

The other number (y) can be obtained using the formula:

=> (GCF x LCM) / X

=> (14 X 168)/ 56

=> 2352/56

=>42

Option B is correct

answer:

-29

step-by-step explanation:

you need a graphing calculator.

so, let's start by setting up a table (for my sake because that text is confusing)

x       f(x)      g(x)      h(x)

-3      12        39          -14

0       0         3           1

1        0         7           -2

3       6        39         -20

okay, that's out of the way. now, your equation is 2 * f(3) - 3 * g(1) + h(3).

for f(3), we look at the chart to see which f(x) value matches x=3.

f(3) = 6

same with g(1) and h(3)

g(1) = 7

h(3) = -20

now, replacing the functions(x) with their numbers is the next step.

2 * 6 - 3 *7 + (-20)

(2*6) - (3*7) - 20

(12) - (21) - 20 = -29

Answer:

D

Step-by-step explanation:

The unit price of the oranges bought by the three friends is $3.50 per pound.

Lamar bought 2 pounds for $7 , unit price = 7 / 2 = $ 3.5 per pound

Enrico bought 5 pounds for $17.50 , unit price = 17.50 / 5 = $ 3.5 per pound

Anna bought 3 pounds for $10.50 , unit price = 10.5/ 2 = $3.5 per pound

Hence we can see that the unit price rate for the oranges is $3.50 .

The average price of a product is calculated by dividing the total sales income by the number of units sold. Managers must supply "similar" units when a single product is given in many variations, such as different bottle sizes.

By weighting different unit selling prices higher by unit sales mix (%) for each single variant, the determination of average pricing is made practicable. We obtain pricing per statistical unit when we employ a standard rather than a genuine range of sizes and product types.

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Answer:

No

Explanation:

To determine if the lengths form the side of a right triangle, use the Pythagorean Theorem:

Substitute 15,11 and 4 into the formula:

Since the Pythagorean Theorem does not hold, the side lengths(15,11,4) do not represent the lengths of the sides of a right triangle.

Answer:

X / 4 + 22

Step-by-step explanation:

22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.

[tex]\fbox{20.25}[/tex]

To find her miles per hour, we need to divide the total miles by the total hours to find how many miles she drives in each hour.

[tex]162\div8[/tex]

[tex]=20.25[/tex]