With the information which of these conclusions is reasonable

QUESTION 4.

The given function is [tex]f(x)=48x^2-32x[/tex].

The highest common factor is [tex]16x[/tex].

We factor to obtain;

[tex]f(x)=16x(3x-2)[/tex]

QUESTION 5

The given function is

[tex]g(x)=20x^2-8x[/tex]

The highest common factor is 4x.

We factor to obtain;

[tex]g(x)=4x(5x-2)[/tex]

QUESTION 6.

The given function is [tex]h(x)=42x^3-35x^2[/tex].

The highest common factor is 7x.

We factor to obtain;

[tex]h(x)=7x^2(6x-5)[/tex]

[tex]\bf \cfrac{32}{100}\div \cfrac{4}{4}\implies \cfrac{32}{100}\div 1\implies \cfrac{32}{100}\implies \cfrac{\underline{2\cdot 2}\cdot 2\cdot 2\cdot 2}{\underline{2\cdot 2}\cdot 5\cdot 5}\implies \cfrac{2\cdot 2\cdot 2}{5\cdot 5}\implies \cfrac{8}{25}[/tex]

Answer:

8/25

Step-by-step explanation:

you divide 32/100 by 4/4=8/25 because 8x4=32 and 4x25=100

Answer:

15 cm

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

[tex]\frac{BC}{EF} =\frac{AC}{DF}[/tex].

[tex]\frac{18}{x}=\frac{12}{10}[/tex]

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

[tex]\frac{18}{x}=\frac{12}{10}\\ 18*10 = x*12 \\ 180 = 12x \\ 15 = x[/tex]

Answer:

Yes, y varies directly with x, and the equation is [tex]y=1.6x[/tex].

Step-by-step explanation:

To check where there is a direct relationship between x and y, we need to check whether all the x,y pairs we have fit some rule:

[tex]y=k\times x[/tex].

For the first pair (x=4, y=6.4),

[tex]6.4=k\times 4[/tex]

Therefore [tex]k = 1.6[/tex].

For the second pair (x=7, y=11.2),

[tex]11.2=k\times 7[/tex]

Therefore [tex]k = 1.6[/tex].

For the third pair (x=10, y=16),

[tex]16=k\times 10[/tex]

Therefore [tex]k = 1.6[/tex].

For the second pair (x=13, y=20.8),

[tex]20.8=k\times 13[/tex]

Therefore [tex]k = 1.6[/tex].

So x does directly vary with y, and we have found out that [tex]k=1.6[/tex].

Answer:   [tex]\bold{\dfrac{y}{x}=1.6\quad \text{which is also equivalent to}\quad y=1.6x}[/tex]

Step-by-step explanation:

[tex]\begin {array}{c|c||l}x&y&\dfrac{y}{x}=k\\--&--&-----\\4&6.4&\dfrac{6.4}{4}=1.6\\\\11.2&7&\dfrac{11.2}{7}=1.6\\\\10&16&\dfrac{16}{10}=1.6\\\\13&20.8&\dfrac{20.8}{13}=1.6\\\end{array}\\[/tex]

Since the k-value is the same for every value in the table, we can conclude that y varies directly with x and the constant of variation k = 1.6  

Answer:

AC

Step-by-step explanation:

Looking at triangles ABD and ACD, they appear to be congruent. This means they have corresponding or matching parts which are equal and form each triangle.

The segment AB is the shortest segment of triangle ABD. It matches to the shortest segment in ACD. This segment is AC.

Answer:

AB <--> AC

Step-by-step explanation:

Hello! Segment AB is congruent to segment AC in ABD and ACD.

Thus, they are in correspondence to one another.

Hope this helps!

f(5) is basically another way of saying x = 5, so we can plug 5 as x into the equation.

3(5) + 2

The answer is D. 17

Answer:

f(5) is basically another way of saying x = 5, so we can plug 5 as x into the equation.

3(5) + 2

The answer is D. 17

Step-by-step explanation:

Answer:

c = 5

Step-by-step explanation:

This is the classic problem that the ancients (particularly the Egyptians) used extensively. When the Nile over flowed in spring, the land had to be reclaimed and  surveyed in the early summer for planting. The 3-4-5 triangle was used to determine right angles for surveying purposes.

Formula

c^2 = a^2 + b^2

Givens

a = 3

b = 4

c = ?

Solution

c^2 = 3*3 + 4*4

c^2 = 9 + 16

c^2 = 25

Take the square root of both sides

To take the square root on your calculator, find the √ on the key pad. Some calculators give it a key and some have the symbol on the body of the calculator. If has its own key do it like this.

√

25

=

The answer should come up as five. If the √ is on the body of the calculator, then

2nd F

√

25

=

The same 5 will come up.

Answer

c = 5

The hypotenuse c of a right triangle with legs a = 3 and b = 4 can be found using the Pythagorean theorem, yielding c = 5

To solve for c, the hypotenuse of a right triangle when given the legs a and b, we utilize the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This is expressed as a² + b² = c².

To solve for c when a = 3 and b = 4, we substitute these values into the theorem to get 3² + 4² = c², which simplifies to 9 + 16 = c². When we combine the values we get 25 = c². Finally, we take the square root of both sides to solve for c, resulting in c = 5.

ANSWER

[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]

EXPLANATION

The given functions are;

[tex]f(x) = \frac{1}{2} x[/tex]

[tex] {f}^{ - 1} (x) = 2x[/tex]

[tex]f( {f}^{ - 1} (x)) = f(2x)[/tex]

[tex]f( {f}^{ - 1} (x)) = \frac{1}{2} \times 2x = x[/tex]

Also,

[tex] {f}^{ - 1}( f(x)) = {f}^{ - 1} ( \frac{1}{2} x)[/tex]

[tex]{f}^{ - 1}( f(x)) = 2 \times \frac{1}{2} x = x[/tex]

In general,

[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]

I can't read number 15, but number 16 is C

[tex] {8}^{2} + {15}^{2} = 64 + 225 = 289 \\ {17}^{2} = 289 \\ \Rightarrow {8}^{2} + {15}^{2} = {17}^{2} \\ \Rightarrow A \: right \: triangle[/tex]

Answer:Yes

Step-by-step explanation:

a^2 + b^2 = c^2

C is the hypotenuse which is the longest side, b is the second longest and a is the shortest one

Answer:

John gave Fred $48

Step-by-step explanation:

Let

x be the amount of dollars John gave fred

y1 be the amount of dollars Fred has at the end

y2 be the amount of dollars John has at the end

Fred has

y1 = - $12 + x

John has

y2 =  $84 - x

y1 = y2

- $12 + x =  $84 - x

2*x = $96

x = $48

3097 is the value you get when rounded off to nearest whole number

The circumference of the circle is found using the formula C = 2 PI r

Circumference = 2 *PI * 15.5 = 31pi

The angle is 90 degrees, which is 1/4 of a complete circle ( 360 degrees).

The arc length would be 1/4 of the circumference:

Arc length = 31pi / 4 = 7.75PI

[tex] \frac{x + 1}{x - 1} > 0 \\ [/tex]

multiply both sides by the x-1 to get rid of the fraction.

[tex]x + 1 > 0 \\ because \: x - 1 \times 0 = 0[/tex]

subtract 1 from each side

x>-1

The solution is

x<−1

x>1

See the image

Answer:

48 X 3= 144 miles

Step-by-step explanation:

Answer:

144 miles

Step-by-step explanation:

First, let's use the distance formula which is distance = rate*time.

We know the rate is 48 miles and the time is 3 hours so if you were to plug it in to the formula you'd get distance = 48*3.

When you multiply 48 by 3 you get 144 which will be the distance.

Answer:

8 units²

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = LK = 7 - 3 = 4 units

and h = J → x- axis = 4 - 0 = 4, hence

A = [tex]\frac{1}{2}[/tex] × 4 × 4 = 8 units²

Answer:

Top- 23 square cm

Bottom- 172.5 square m

Step-by-step explanation:

Let me know if you need an explanation

Answer:

x=4±9i

Step-by-step explanation:

Solve the equation for x by finding a, b, and c of the quadratic then use the qaudratic formula

Answer:

[tex]x=4-9i[/tex] or  [tex]x=4+9i[/tex]

Step-by-step explanation:

The given equation is

[tex]x^2-8x+97=0[/tex]

By comparing to [tex]ax^2+bx+c=0[/tex], we have a=1,b=-8 and c= 97.

The quadratic formula is;

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

We substitute the values to obtain;

[tex]x=\frac{--8\pm\sqrt{(-8)^2-4(1)(97)} }{2(1)}[/tex]

[tex]x=\frac{8\pm\sqrt{-324} }{2}[/tex]

[tex]x=\frac{8\pm18i }{2}[/tex]

[tex]x=4\pm9i[/tex]

Therefore [tex]x=4-9i[/tex] or  [tex]x=4+9i[/tex]

Step-by-step explanation:

1 1/3x=-8/3

Answer:

x=−2 is the answer

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2/3(x - 4) = 2x

(2/3) (x) + (2/3) (-4) = 2x      Distributed

2x/3  +  -8/3 = 2x

Step 2: Subtract 2x from both sides.

2x/3 + -8/3 = 2x

(2x/3) (-2x/1)  + -8/3 =0

-4x/3 + -8/3 = 0

Step 3: Add 8/3 to both sides.

-4x/3 = 8/3

Step 4: Multiply both sides by 3/(-4).

(3/-4)  (-4x/3) = ( 3/-4)  (8/3)

X= -2 because 3 x 8= 24   and  -4 x 3 = -12

24 Divided by -12 give -2

Hopes this helps!

Answer:

[tex]1,125\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces plus the two lateral rectangular faces

so

[tex]SA=2[\frac{1}{2}(15)(15)]+2[(30)(15)]= 1,125\ ft^{2}[/tex]

3 to a negative 3 would be 1/3^3 and then simplify to 1/27 so your answer is D

Answer:

I believe your answer is 429.

Step-by-step explanation:

5 1/2 x 6 1/2 x 12 = 429

Answer:

two $20 and five $10

He has three $20 and four $10. Hope this helps!

Answer:

Step-by-step explanation:

3.14159 is irrational because it's a repeating decimal; it cannot be expressed as the ratio of two integers.  All the others can be expressed in that way.

Answer:

B. would be your answer

The numbers are 19 and 28.

Answer:

28 and 19

Step-by-step explanation:

let the 2 numbers be x and y, x > y, then

x + y = 47 → (1) ← sum of numbers

x - y = 9 → (2) ← difference of numbers

Adding the 2 equations to eliminate y

2x = 56 ( divide both sides by 2 )

x = 28

substitute x = 28 into (1) and solve for y

28 + y = 47 ( subtract 28 from both sides )

y = 47 - 28 = 19

The 2 numbers are 28 and 19

Given:

Brian scored 154 more than Colin

Colin’s score=141

Let Brian’s score be x

x= Colin’s score+ 154

x= 141 + 154

x=295

Brian’s score=x=295

Combined score= Brian’s +Colin’s

Combined score= 436

They have a combined score of 436 points

Data;

Let's write an equation showing Brain's score

[tex]x = 141+ 154\\x = 295[/tex]

Brain's score is equal to 295 points.

The sum of their combined score would be

Collin + Brain

[tex]141+295=436[/tex]

They have a combined score of 436 points.

Learn more on word problem here;

https://brainly.com/question/13818690

Answer:

C. [tex]x>0[/tex]

Step-by-step explanation:

Given: [tex]f(x)=log(8x)[/tex]

To find the domain of a logarithmic function, we need to take the argument, 8x, and set it greater to zero. This is because an argument of a logarithmic function cannot be zero or negative.

[tex]8x>0[/tex]

[tex]x>0[/tex]

So since x is greater than zero, we have just found out our domain:

Interval Notation: (0, ∞)

Set Notation: {[tex]x|x>0[/tex]}

The domain of the logarithmic function is,

⇒ x > 0

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that:

The function is,

⇒ F (x) = log₈ x

Now, To find the domain of a logarithmic function, we need to take the term, 8x, and set it greater to zero.

This is because an argument of a logarithmic function cannot be zero or negative.

Hence, We get;

8x > 0

x > 0

Thus, The domain of the logarithmic function is,

⇒ x > 0

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

Answer:

Option D.

Step-by-step explanation:

Precision refers to the the level of measurement and exactness of a measurement. The mean diference between 'precision' and 'exactness' is that  if a measuring device gives consisten measurements it's considered precise, but it's not necessarily accurate.

For example, a measurement of 2.365m is more precise than a measurement of 2.3m, given that 2.365m has more significant figures and was made with an instrument that has higher precision. This doesn't mean that the measurement is accurate, the real value could be 3m for example! ✅

Answer:

Neither

Step-by-step explanation:

Check if it's arithmetic:

-8, -3, 6, 11, -22

+5  +6   +5  -33

Nope

Check if geometric:

-8, -3, 6, 11, -22

*3/8  *-2 *11/6 *-2

Nope

So it's neither