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Answer:

CB = 7

Step-by-step explanation:

CB = CK

5x - 3 = 3x + 1

5x - 3x = 1 + 3

2x = 4

x = 4 / 2

x = 2

CB = 5x - 3

= 5 ( 2 ) - 3

= 10 - 3

CB = 7

Answer:

CB = 7

Step-by-step explanation:

since the 2 triangles are AAS (B, K, E, CE as shared side) proven congruent, CB and CK must have the same length.

5x - 3 = 3x + 1

2x = 4

x = 2

CB = 5x - 3 = 5×2 - 3 = 10 - 3 = 7

Answer: Third proportion is 21/5.

Step-by-step explanation:

Let the proportion be x

so,

3:5:x:7

so

3:5 = x:7

or, 3/5 = x/7

or, 21 = 5x

or, x = 21/5

Answer:

Leo's weight at the end of the fourth week = 181.7 pounds

Step-by-step explanation:

Leo's initial weight = 190 pounds

First week = lost 4.3 pounds

New weight = 190 pounds - 4.3 pounds

= 185.7 pounds

Second week = lost 2.8 pounds

New weight = 185.7 pounds - 2.8 pounds

= 182.9 Pounds

Third week = gained 0.7 pounds

New weight = 182.9 pounds + 0.7 pounds

= 183.6 pounds

Fourth week = lost 1.9 pounds

New weight = 183.6 pounds - 1.9 pounds

= 181.7 pounds

Leo's weight at the end of the fourth week = 181.7 pounds

Alternatively

New weight = initial weight - first week - second week + third week - fourth week

= 190 - 4.3 - 2.8 + 0.7 - 1.9

= 181.7 pounds

There are two triangles here: ABC and ADF. These triangles are similar, and thus proportional. So, we can set up a proportion between the left side of each triangle and the base of each triangle.

AB / AD = BC / DE

4 / (4 + BD) = 5 / 9

---AD is made up of AB and DB. We know AB, but not BD, so we need to find its value to find the length of AD.

5(4 + BD) = 9 x 4

20 + 5BD = 36

5BD = 16

BD = 3.2

AD = AB + BD

AD = 4 + 3.2

AD = 7.2

Hope this helps!

Answer:

I assume that we want to complete the statement:

"The maximum profit of $__ dollars is reached when __ items are produced"

We know that the profit equation is defined between x = 0 and x = 100, which are the two roots of the equation (so the profit is equal to zero for x = 0 and for x = 100).

Then we can assume that the profit will be positive in this range.

Thus, the quadratic equation should have a negative leading coefficient, which would mean that the arms of the graph go downwards.

If this is the case, we know that the maximum will be at the vertex.

Here we know that the vertex is:

(50, 1000)

Where remember, x represents the number of items and y represents the profit.

So, given that the maximum is at the vertex, and we know that the vertex is (50, 1000) we can conclude that the maximum profit is $1000, and this happens when the number of produced items is 50.

Then the complete statement is:

"The maximum profit of $1000 dollars is reached when 50 items are produced"

Answer:

Part A: One | Part B: x = 4

Step-by-step explanation:

[tex]3(2x-7)=3\\6x-21=3\\6x=24\\x=4[/tex]

Answer:

4

Step-by-step explanation:

3(2x _7)=3

multiply 3 by everything in the bracket

6x-21 = 3

move 21 to the other side of the equation,it becomes positive sine it crosses the = sign

6x = 3+21

6x =24

divide both sides by 6

6x/6=24/6

x = 4

Answer:

y = -4x

Step-by-step explanation:

First, for an equation of form y=mx+b, m represents the slope. Therefore, for y=x/4+2 = (1/4)*x + 2, 1/4 is the slope. For perpendicular lines, the negative reciprocal of the slope is the slope of the line perpendicular to it. Therefore, the slope of our line is the negative reciprocal of 1/4.

To find the reciprocal of something, we can just divide 1 by it (another way to do this would be to flip the numerator and denominator, so 1/4 turns into 4/1). Therefore, 1/(1/4) = (1/1)/(1/4) = (1/1) * (4/1) = 4. The negative reciprocal is thus -4.

Our equation is therefore of form y = (-4) x + b. To solve for b, we can plug in the point given and solve for b in our equation. We have

-4 = (-4) * 1 + b

-4 = -4 + b

add 4 to both sides to isolate the b

0 = b

Therefore, our equation is

y= (-4)x + 0

y = -4x

Step-by-step explanation:

[tex] \frac{1}{16} = {2}^{ - 4} [/tex]

Answer:

2^-4

Step-by-step explanation:

16 = 2^4

1/16 = 1/2^4

We know 1/a^b = a^-b

1/2^4 = 2^-4

Answer:

A =136 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) *h  where b1 and b2 are the lengths of the bases and h is the height

A = 1/2( 22+12) *8

A = 1/2 ( 34)*8

A =136 cm^2

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

Explanation:

Refer to the diagram below.

There's a lot of info given to us that we don't need (and won't use).

The only key piece of info we'll really use is the fact that angle XZY is 27 degrees.

Draw in segments RU and RT to form quadrilateral TRUZ

Focusing solely on this quadrilateral, we see that the angles T and U are 90 degrees each (since the tangents are perpendicular to the radii at the point of tangency). Furthermore, we see that angle Z is 27 while angle R is x

For any quadrilateral, the four angles always add to 360 degrees

T+R+U+Z = 360

90+x+90+27 = 360

x+207 = 360

x = 360-207

x = 153

That means angle R of quadrilateral TRUZ is 153 degrees.

Furthermore, it means angle TRU is 153 degrees.

By extension, it indicates that minor arc TU is 153 degrees.

That makes arc TSU = 360 - (minor arc TU) = 360 - 153 = 207 degrees

By Joining TR and UR we got 2 right angles and a Quadrilateral

now

In a Quadrilateral sum of angles=360°

[tex]\\ \large\sf\longmapsto x+90+90+27=360[/tex]

[tex]\\ \large\sf\longmapsto x+180+27=360[/tex]

[tex]\\ \large\sf\longmapsto x+207=360[/tex]

[tex]\\ \large\sf\longmapsto x=360-207[/tex]

[tex]\\ \large\sf\longmapsto x=153°[/tex]

Answer:

80ft

Step-by-step explanation:

1ib=4ft, multiply by 20 both sides and you will get 20in=80ft

Answer:

8.80

Step-by-step explanation:

(S. D.)^2=summation(x-mean)^2/(n-1)

S. D.=sqrt(388/5)

S. D.=8.80

Answer:

p = -2

Step-by-step explanation:

px + 2y + 8 = 0

px + 2y  = -8

p(4)    = -8

p = -2

Answer:

Value of tan( π/3 ):

[tex]{ \tt{ \frac{\pi}{3} = \frac{180}{3} = 60 \degree }}[/tex]

60° lies within the first quadrant.

[tex]{ \sf{ \tan( \frac{ \pi}{3} ) = ( \frac{1}{2} , \: \frac{ \sqrt{3} }{2}) }}[/tex]

Since it's a half:

[tex]{ \boxed{ \sf{ \tan( \frac{\pi}{3} ) = \sqrt{3} }}}[/tex]

Length of hypotenuse:

[tex]{ \bf{ \sin(31 \degree) = \frac{16.5}{h} }} \\ { \sf{h = 32.04}}[/tex]

Hypotenuse = 32.0

Answer:

225 degrees

Step-by-step explanation:

Given the following data;

To find the angle in degrees subtended by an arc;

Mathematically, the length of the arc of a circle is given by the formula;

S = rA

Where;

Substituting the values into the formula, we have;

22 = 5.6 * A

[tex] A = \frac {22}{5.6} [/tex]

A = 3.9286 radians.

Next, we would convert the value of the angle in radians to degrees;

Conversion:

[tex] 1 \; radian = \frac {180}{\pi} \; degrees [/tex]

[tex] 3.9286 \; radians = X \; degrees [/tex]

Cross-multiplying, we have;

[tex] X = \frac {180}{\frac {22}{7}} * 3.9286 [/tex]

[tex] X = \frac {180 * 7}{22} * 3.9286 [/tex]

[tex] X = \frac {1260}{22} * 3.9286 [/tex]

[tex] X = 57.2727 * 3.9286 [/tex]

X = 225.0015 ≈ 225 degrees

Answer:

0, 1.32

Step-by-step explanation:

16cos(t)*sin(t)=4sin(t)

cos(t)=1/4 or sin(t)=0

t=1.32 or 0

Answer:

Step-by-step explanation:

The answer is D. Use the Stat and then Edit button on your TI calculator to edit the values in L1 and L2 tables. In L1 enter 0, 1, 2, 3, 4, 5 and then arrow over and enter the y values into L2 the same way. Enter the number 12, then hit enter; enter the number 14, hit enter; enter the number 15 and then hit enter, etc. Do the same for the values that are going into L1.

When that is done, hit the Stat button again and arrow down to QuadReg and hit enter. Depending upon your calculator, you may have to arrow down to "calculate" or the calculator may display the equation immediately after hitting QuadReg. Again, it all depends upon your calculator.

The required correct quadratic regression equation that fits the given data is y = -0.89x² + 3.24x+11.93. Option D is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
To find the quadratic regression equation, we need to use a calculator or software that can perform a quadratic regression analysis. Using such a tool, we obtain the following equation:

y = -0.89x² + 3.24x+11.93

This equation fits the data points (0, 12), (1, 14), (2, 15), (3, 14), (4, 10), and (5, 6) with a high degree of accuracy.

The equation is in the form of a quadratic function, which has a parabolic shape when graphed. The coefficient of the x² term (-0.89) indicates that the parabola is downward-facing, while the other coefficients determine the exact shape and position of the parabola.

Option A is incorrect because its equation does not fit the data points accurately. Option B is also incorrect because it is not a quadratic equation, and option C is incorrect because its equation also does not fit the data points accurately.

Learn more about equations here:

brainly.com/question/10413253

#SPJ7

Answer:

[tex]15x^2 + 8x -12[/tex]

Step-by-step explanation:

(5x+6)(3x-2)

"foil" it out

F: 5x * 3x  = 15x^2

O: 5x * -2  = -10x

I: 6*3x = 18x

L: 6 * -2 = -12

Answer:

15x² + 8x - 12

Step-by-step explanation:

(5x + 6)(3x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

5x(3x - 2) + 6(3x - 2) ← distribute both parenthesis

= 15x² - 10x + 18x - 12 ← collect like terms

= 15x² + 8x - 12

Answer:

SSS Postulate

Step-by-step explanation:

The first says 2 sides are the same

The second says 2 sides are the same

The last says 2 sides are the same

Side side side

SSS Postulate

Answer:

The x-coordinate is –4

The y-coordinate is –1

The point is in the quadrant Third quarter ( 3 )

I hope I helped you^_^

Answer:

A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.

The choose (D)

(0,-4) and (2,0)

Answer:

-2, 6, 20 ,...

Step-by-step explanation:

3n² +5n -2

if n=0 , then 3*0² +5*0 -2= -2

if n=1, then 3*1² +5*1 -2 = 3+5-2 = 6

if nu 2, then 3*2² +5*2 -2 = 12 +10 -2 = 20

Answer:

10 feet

Step-by-step explanation:

let the ladder be x feet in length

Using the Pythagoras theorem,

6^2+(x-2)^2=x^2

if you solve this you'll get, x = 10

Answered by GAUTHMATH

Answer:

Quelles caractéristiques ces mots ont-ils en commun ? Cliquez sur tout ce qui s'applique.

Step-by-step explanation: