The triangles in the picture are congruent by which method

Answer:

[tex]y = 4^x[/tex]

Step-by-step explanation:

Given

[tex](2,16)[/tex]

[tex](5,1,024)[/tex]

Required

Determine the exponential function [tex]y = a.b^x[/tex]

In [tex](2,16)[/tex]

[tex]x=2[/tex] and [tex]y = 16[/tex]

Substitute these values in [tex]y = a.b^x[/tex]

[tex]16 = a.b^2[/tex] --- (1)

In [tex](5,1,024)[/tex]

[tex]x = 5[/tex] and [tex]y = 1024[/tex]

Substitute these values in [tex]y = a.b^x[/tex]

[tex]1024 = a.b^5[/tex] --- (2)

Divide (2) by (1)

[tex]\frac{1024}{16} = \frac{a.b^5}{a.b^2}[/tex]

[tex]\frac{1024}{16} = \frac{b^5}{b^2}[/tex]

[tex]64 = \frac{b^5}{b^2}[/tex]

Apply second law of indices

[tex]64 = b^{5-2[/tex]

[tex]64 = b^3[/tex]

Express 64 as an exponent of 3

[tex]4^3 = b^3[/tex]

[tex]4 = b[/tex]

[tex]b = 4[/tex]

Substitute 4 for b in (1)

[tex]16 = a.b^2[/tex]

[tex]16 = a * 4^2[/tex]

[tex]16 = a * 16[/tex]

[tex]16 = 16a[/tex]

Solve for a

[tex]a=\frac{16}{16}[/tex]

[tex]a = 1[/tex]

Substitute 1 for a and 4 for b in [tex]y = a.b^x[/tex]

[tex]y = 1 * 4^x[/tex]

[tex]y = 4^x[/tex]

The exponential function is given by y = 100(0.4)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the factor.

At point (2, 16):

16 = ab²      (1)

At point (5, 1.024):

1.024 = ab⁵      (2)

Dividing equation 2 by equation 1:

b³ = 0.064

b = 0.4

16 = a(0.4)²

a = 100

The exponential function is given by: y = 100(0.4)ˣ

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Answer:

Answer:

3

Step-by-step explanation:

slop of given point is 3

D. The function shown on the graph has a smaller rate of change and a lower starting point. Sorry if incorrect i hope i helped.

Answer:

um 3

Step-by-step explanation:

whats 24 divided by 3 mate? 3

i mean all u need is a calculator im dumb as hell and i know that...

hope...this helps you :) have a great day

Answer:

FOIL

Step-by-step explanation:

" is just a mnemonic. It helps some people to remember all the steps needed to multiply two binomials. It "makes sense" because it's methodical and gives the right answer.

Answer:

∠ EFG = 83°, ∠ GCE = 97°

Step-by-step explanation:

Since FE and FG are tangents to the circle then

∠ FGC and ∠ FEC are right angles

The sum of the angles in quadrilateral CEFG = 360°

Sum the 4 angles and equate to 360

3x + 11 + 90 + 5x - 23 + 90 = 360, that is

8x + 168 = 360 ( subtract 168 from both sides )

8x = 192 ( divide both sides by 8 )

x = 24

Thus

∠ EFG = 3x + 11 = 3(24) + 11 = 72 + 11 = 83°

∠ GCE = 5x - 23 = 5(24) - 23 = 120 - 23 = 97°

do u like beans?Step-by-step explanation: hope it helps

Answer:

-0.2z

Step-by-step explanation:

-0.5z + 0.9z - ( -0.3z+0.9z) open paranthesis and change the sign of all terms

-0.5z + 0.9z + 0.3z - 0.9z combine terms

-0.5z+0.3z= -0.2z

Answer:

After the first day, 1/3 of the original amount remained:

... (1/3)·45 = 15

After the second day, 2/3 of that amount remained:

... (2/3)·15 = 10

The bookstore has 10 copies left.

Step-by-step explanation:

Answer:

Step-by-step explanation:

45 copies and sold 2/3= 30 sold so 15 left

15 copies and sold 2/5= 6 sold so 9 left

Answer:

56, 112, 168, 224, and more

Answer:

120

Step-by-step explanation:

14-6=8x15=120

Answer:

70 miles

Step-by-step explanation:

Divide 42 by 0.60 = 70

Multiply 70 * 0.60 = 42.

Answer:

The equation of a line that is parallel to x−2y=−4 and passes through the point (0, 0) will be:  [tex]x-2y=0[/tex]

Step-by-step explanation:

Given the line

[tex]x-2y=-4[/tex]

[tex]x+4 = 2y[/tex]

[tex]y=\left(\frac{1}{2}\right)x+2[/tex]

[tex]m_1=\frac{1}{2}[/tex]

so, the slope of the line parallel to the given line would have

the same slope as  [tex]\frac{1}{2}=m[/tex], and passed through the point (0, 0).

Therefore, the equation of the required line is given by

[tex]y = mx+b[/tex]

[tex]y=\left(\frac{1}{2}\right)x+0[/tex]

[tex]y=\left(\frac{1}{2}\right)x[/tex]

[tex]2y=x[/tex]

[tex]x-2y=0[/tex]

Therefore,  the equation of a line that is parallel to x−2y=−4 and passes through the point (0, 0) will be:  [tex]x-2y=0[/tex]

Answer:

First =  Poppy seed  = 3x10^-4 grams  = 0.0003 grams

Second  =  sesame seeds  =  3.64x10^-6 grams  = 0.00364 grams

third  = 250 pumpkin seeds 21 grams  = one seed 0.084 grams

Step-by-step explanation:

3.64x10^-6 kilograms *1000gr/Kilograms =  0.00364 grams

21/250 = 0.0084 grams one seeds

Answer:

$150

Step-by-step explanation:

5 x 6 = 30

25 x 6 = 150

Answer:

If it is a solution of equations, then plug your solution into the equations you are working on to make sure that all equations are satisfied by your solution.

Step-by-step explanation:

I hope that this was helpful.

Answer:

[tex]f^{-1} (x)=x^{2} -3[/tex]

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=\sqrt{x+3}[/tex]

We can find the inverse function by exchanging x and y, and then solve for y.

[tex]y=\sqrt{x+3}[/tex]

Replace x with y.

[tex]x=\sqrt{y+3}[/tex]

square both sides

[tex]x^2=y+3[/tex]

[tex]y=x^2-3[/tex]

Hence,

[tex]f^{-1} (x)=x^{2} -3[/tex]

Answer:

slope: 0.05

y-intercept: 320

Step-by-step explanation:

y is the total weekly salary and x is the sales

there is a constant salary of $320, which will be the constant in the equation.

y = mx + b

y = mx + 320

we know there is a 5% commission on all sale, which we can convert to the fraction 0.05.

y = .05x + 320

Now we can see that the slope is .05 and the y-intercept is 320

Answer:

Step-by-step explanation:

Given

Length of the ladder = 12foot

angle of elevation = 80 degrees

Required

Height of the wall (opposite side)

The set up will form a right angled triangle where

length of the ladder is the hypotenuse

height of the wall is opposite;

Using SOH, CAH, TOA trig identity

According to SOH

sin 80 = opp/hyp

sin80 = opp/12

opp = 12sin80

opp = 11.82 feet

Hence the height of the wall is 11.8feet (to the nearest tenth)

Answer:

4.7

Step-by-step explanation:

4.69041575982

Round to 4.7

Answer:

Option B: f(x) = 2x2 + 2x – 4

Step-by-step explanation:

f(x)=x²-4x-5 is the polynomial function of the given graph.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

We need to find the polynomial of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

When x=0, then y should be -5.

This can be satisfied by f(x)=x²-4x-5 and  f(x)=-x²-4x-5

Now let us find the value of y when x is 2.

When x is 2 the value of y should be -9 by the given graph

f(x)=x²-4x-5

=4-8-5

=-9

Hence, f(x)=x²-4x-5 is the polynomial function of the given graph.

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Answer:

3rd quadrant

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Answer:

-27 maybeeeeeeeeeeeee

Answer:

Step-by-step explanation:

4= 0 degree

2z= 1 degree

4r^2st^3= 6 degree

3xyz^2= 4 degree

The to your problem is m = -3, I hope this really helps you :)

Y= -3x+5 that’s the answer I got

Answer:

\tan \left(\frac{\sin \left(x\right)-\cos \left(x\right)}{\cos \left(x\right)+\sin \left(x\right)}\right)

Step-by-step explanation:

Answer:

Ok im too too sure but I think that it is the one with the filled in dot -->

Step-by-step explanation:

Answer:

-6 < x < 1

Step-by-step explanation:

-14 < 10 + 4x < 14

Subtract 10 from both sides

-24 < 4x < 4

Divide both sides by 4

-6 < x < 1

Answer: - 6 < x < 1

|10 + 4x| < 14

⇔ -14 < 10 + 4x < 14

⇔ -14 - 10 < 4x < 14 - 10

⇔ - 24 < 4x < 4

⇔ -24/4 < x < 4/4

⇔ - 6 < x < 1

Step-by-step explanation:

Answer:

This is incorrect.  

Step-by-step explanation:

You move the decimal 7 places to the right after the 7.  Since 2 is the third digit, you're adding 4 more zeros.