A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8). What is the corresponding quadratic expression? A. 2x2 − 16x + 24 B. -2x2 + 16x – 24 C. -2x2 - 16x + 24 D. -x2 − 16x + 12 E. -x2 − 16x – 24

Respuesta:

6 cm

Explicación paso a paso:

Paso 1: Información provista

Longitud de la hipotenusa (h): 10 cm

Longitud del cateto 1 (c₁): 8 cm

Paso 2: Calcular la longitud del cateto 2 (c₂)

Tenemos un triángulo rectángulo, es decir, que uno de sus ángulos es 90°. Conociendo la hipotenusa y uno de los catetos, podemos determinar la longitud del otro cateto usando el Teorema de Pitágoras.

h² = c₁² + c₂²

c₂² = h² - c₁²

c₂ = √(h² - c₁²)

c₂ = √((10 cm)² - (8 cm)²) = 6 cm

Answer:

a. x= 9

b. 70

c. 110

d. 70

e. 110

Step-by-step explanation:

a.

congruent angles have the same measure. 1 and 3 are congruent and 2 and 4 are congruent

2(12x+2)+2(7x+7)=360

divide both sides by 2

12x+2+7x+7=180

combine like terms

2+7=9

12x+7x=19x

19x+9=180

subtract both sides by 9

19x=171

divide both sides by 19

x=9

7x+7,

7*9+7

63+7 = 70

1 is 70, 3 is 70

12x+2, x=9

108+2 = 110

2 and 4 is 110

Answer:

Step-by-step explanation:

Angles 1 and 2 are supplementary (their sum is 180 degrees)

7x + 7 + 12x + 2 = 180

19x= 171

x = 9

m 1 = 7 * 9 + 7 = 70 degrees

m 2 = 12 * 9 + 2 = 108 + 2 = 110 degrees

m 3 = angle 1 and angle 3 are vertical, so they have the same measure: 70 degrees.

m 4 = angle 2 and angle 4 have the same measure: 110 degrees

Answer:

2, 5, 6

Step-by-step explanation:

The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where all variables to the right are dimensions of the prism.

Therefore, we're looking for three numbers that multiply to be 60.

Since the question stipulates that no side length may be 10, we have:

[tex]2\cdot 5\cdot 6=60[/tex]

Answer:

Step-by-step explanation:

Least to largest:

First compare the whole parts of the decimal number. The whole part with greater number will be the greatest number.

2) Then compare the decimal parts. Compare tenth place. The decimal number that has greater number in the tenth place will be greater.

3) If the number in  tenth place is equal, then compare 100th place and so on

A) 15.99  ; 16  ; 16.02  ; 16.2

B) 4.45  ; 4.9945  ; 5.545   ; 5.56

c) 44.11  ; 44.5  ; 45 ; 45.01

D) 8.995 ;   9.0599  ;  9.27  ;  9.6

Greatest to least

A) 2.111   ; 2.11   ; 2.1   ; 2.01

B) 32.32  ; 32.302     ; 32.032  ; 3.99

c) 7.666  ; 7.66  ;  7.6  ; 7.06

D) 57.68  ; 57.57   ;   57.057   ; 5.75

Answer:

f(x) = x³ - 3

Step-by-step explanation:

Given f(x) then the graph of f(x) + c represents a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < o then a shift down o c units

Here a shift down of 3 units, hence c = - 3, thus

f(x) = x³ - 3

Answer:

See explanation below

Step-by-step explanation:

Flat fee = $25

Cost per mile = $0.60

Let

C = total cost

m = number of miles travelled by the truck

The equation is

C = 25 + 0.60m

The independent variable is miles,m travelled

The dependent variable is total cost, C

$25 is the constant

Answer:

4th option 0,5,10,15

Step-by-step explanation:

Let's check if the first choice is geometric.

2*3 = 6. is 6*3 = 18, yes! is  18*3 = 54. Yep! its geometric

the second option multiplies by -2, it is geometric

the third option multiplies by 1/5, it is geometric

The fourth option does not multiply by anything common, it is Not geometric

Answer:

0,5,10,15 is not the sequence of geometric.

Generally, to check whether a given sequence is geometric, one simply checks whether successive entries in the sequence all have the same ratio. The common ratio of a geometric series may be negative, resulting in an alternating sequence.

Step-by-step explanation:

This is totally correct!

Answer:

i hope this helps you

Step-by-step explanation:

answer is c

Answer:

Step-by-step explanation:

the square of x-5 given by

[tex] \displaystyle (x - 5) ^{2} [/tex]

use (a-b)²=a²-2ab+b² to simplify so we obtain:

[tex] \displaystyle {x}^{2} - 10x + 25[/tex]

hence

our answer is 2)

to find:

[tex]f(x) - g(x)[/tex]

substitute the value of f(x) and g(x):

[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - ( {2x}^{2} - 4x + 4)[/tex]

remove parentheses and change its sign:

[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - {2x}^{2} + 4x - 4[/tex]

combine like terms:

[tex] \rm \displaystyle{6x}^{2} + 12x - 5 - {2x}^{2} - 4[/tex]

collect like terms:

[tex] \rm \displaystyle{4x}^{2} + 12x -9[/tex]

hence,

our answer is 3)

given Polynomial:

[tex] \displaystyle {5x}^{3} + 2 {x}^{2} + 7[/tex]

substitute the value of x:

[tex] \displaystyle {5.(10}^{3}) + 2 ({10}^{2}) + 7[/tex]

simplify squares:

[tex] \displaystyle 5(1000) + 2 (100) + 7[/tex]

simplify multiplication:

[tex] \displaystyle 5000 + 2 00 + 7[/tex]

simplify addition:

[tex] \displaystyle 5207 [/tex]

hence our answer is 1)

given:

notice that,

every time there's a GCF of 4x²y

hence our answer is 4)

Answer:

240 degrees

Step-by-step explanation:

360 - 120 = 240

Answer:

240° i think

Answer:

Exponential

Step-by-step explanation:

Linear is easy to remember because it goes in a straight LINE.

Only other option is a quadratic and this does not create a parabola

Answer:

46°

Step-by-step explanation:

D = 90° - 44° = 46°

Answer:

45%

Step-by-step explanation:

Answer:

The unit rate is, $1.95

Step-by-step explanation:

7.80 ÷ 4= 1.95

So , unit  rate is  [tex]\frac{1}{1.95\\}[/tex]

Answer:

4.5 miles per hour

Step-by-step explanation:

Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?

Distance = 3/4 of a mile

Time taken on Monday = 1/6 of an hour.

What is Selma's unit rate in miles per hour for Monday's run?

Unit rate in miles per hour for Monday's run = distance ÷ time taken

= 3/4 ÷ 1/6

= 3/4 × 6/1

= (3 * 6) / (4 * 1)

= 18/4

= 4.5 miles per hour

Unit rate in miles per hour for Monday's run = 4.5 miles per hour

Answer:

6.5

Step-by-step explanation:

Cos = Adjacent/Hypotenuse

For the angle with the measure of 70°

Adjacent = x

Hypotenuse =  19

Hence, cos 70 = x/19

multiply both sides by 19

cos(70) * 19 = 19cos(70)

x/19 * 19 = x

we're left with x = 19cos(70)

19cos(70) = 6.5 ( rounded to the nearest tenth )

x = 6.5

I hope this is help full to u

thank you

Answer:

0.6 or [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) we get that the hypotenuse is 5.

so the cos V is adjacent over the hypotenuse. so if adjacent is 3 and hypotenuse is 5, the answer is [tex]\frac{3}{5}[/tex] which equals 0.6 in decimal form.

Answer:

Step-by-step explanation:

In similar triangles corresponding triangles are in same ratio.

[tex]\frac{15}{5}=\frac{12}{y}[/tex]

Cross multiply,

15 * y = 12 * 5

     y = [tex]\frac{12*5}{15}[/tex]

      y = 4

Step-by-step explanation:

line a is perpendicular to B.

if the slope of line A is -3/4 what is the line of B

a²+b²=c²

5²+9²=c²

25²+81²=c²

106=c²10.2

5

Answer:

  They represent positive and negative numbers.

Step-by-step explanation:

Answer:

120 ways

Step-by-step explanation:

Here, we are looking at arranging around a table

To do this, we sit down one of the children and arrange the remaining around the one that we have sat down

In scenario like this, the number of possible arrangement ways will be;

(n-1)! ways

where n is the number of children which is 6 in this case

So the possible number of ways will be;

(6-1)! = 5! = 120 ways

Answer:

[tex]z = (6,-1)[/tex]

Step-by-step explanation:

The missing parameters are:

[tex]x = (3,-1)[/tex]

[tex]y = (3,5)[/tex]

[tex]yz= \sqrt{45[/tex] --- Hypotenuse

Required

The coordinate of Z

First, calculate the distance xy

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

[tex]xy = \sqrt{(3 - 3)^2 + (-1 - 5)^2}[/tex]

[tex]xy = \sqrt{0 + 36}[/tex]

[tex]xy = \sqrt{36}[/tex]

[tex]xy = 6[/tex]

By Pythagoras theorem, distance xz is:

[tex]yz^2 = xz^2 + xy^2[/tex]

[tex](\sqrt 45)^2 = xz^2 + 6^2[/tex]

[tex]45 = xz^2 + 36[/tex]

Collect like terms

[tex]xz^2 =45-36[/tex]

[tex]xz^2 =9[/tex]

[tex]xz = \sqrt{9}[/tex]

[tex]xz = 3[/tex]

This means that z is 3 units to the right of x

We have:

[tex]x = (3,-1)[/tex]

The rule to determine z is:

[tex](x,y) \to (x + 3, y)[/tex]

So, we have:

[tex]z = (3 + 3,-1)[/tex]

[tex]z = (6,-1)[/tex]

Answer:

obtuse angle is 2 and acute angle is 1

Step-by-step explanation:

Obtuse Angle: An angle between 90 and 180 so angle 2 is an obtuse angle

Acute Angle: An angle between 0 and 90 so angle 1 is an acute angle