bruce banner had a taxable income last year of $43,467. his state's income tax rate is 3.9% and his city income tax is 1.8%. what total state and city income taxes did bruce pay last year?

Since QC and BR are parallel, triangles CDQ and BDR are similar.

This means that corresponding sides are in proportion, so we have

[tex] BD \div QD = RD \div CD [/tex]

Substituting numbers, we have

[tex] 26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x} [/tex]

Multiply both sides by [tex] 39x [/tex]

[tex] 65x = 39(18+x) [/tex]

Expand right hand side:

[tex] 65x = 702 + 39x [/tex]

Subtract 39x from both sides:

[tex] 26x = 702 [/tex]

Divide both sides by 26

[tex] x = \dfrac{702}{26} = 27 [/tex]

Just took the test and got the the correct answer *\(♡°▽°♡)/*

Look at the image down below!!

Answer:

{x = 1/7 ,y = 1

Step-by-step explanation:

Solve the following system:

{-5 y = -5 | (equation 1)

{7 x + 6 y = 7 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 6 y = 7 | (equation 1)

{0 x - 5 y = -5 | (equation 2)

Divide equation 2 by -5:

{7 x + 6 y = 7 | (equation 1)

{0 x+y = 1 | (equation 2)

Subtract 6 × (equation 2) from equation 1:

{7 x+0 y = 1 | (equation 1)

{0 x+y = 1 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 1/7 | (equation 1)

{0 x+y = 1 | (equation 2)

Collect results:    Answer:    {x = 1/7 ,y = 1

Answer:

No

Step-by-step explanation:

Answer:

b. 3x - (5y -7)

Step-by-step explanation:

Let x represent "a number". Let y represent "another number."

The "3 times a number" is represented by 3x.

And "5 times another number less 7" is represented by 5y -7.

The difference between these quantities is the second subtracted from the first:

... 3x - (5y -7) . . . . matches selection b.

Neither one

Frog A's "unit rate" is ...

... (8 flies)/(4 minutes) = 2 flies/minute

Frog B's "unit rate" is ...

... (14 flies)/(7 minutes) = 2 flies/minute

Both rates are the same. Each frog eats 2 flies per minute.

Answer:

i dont like frogs

Step-by-step explanation:

Answer:

The correct answer would be A) (4, 49.6)

Step-by-step explanation:

In order to find the equation, we first have to start with the base form of direct variation.

y = kx

Now we input the k value.

y = 12.4x

Now that we have this, we can try the ordered pairs and look for which satisfies the equation.

y = 12.4x

49.4 = 12.4(4)

49.4 = 49.4

Since this is the true statement, this is the ordered pair that works.

Answer:

(4,49.6)

Step-by-step explanation:

Answer:

2.5 min

Step-by-step explanation:

The tortoise takes 1 min/3 m.

7.5 × 1/3  = 2.5 min

The number 9.36×10-4 in standard form is 0.000936. You convert from scientific notation to standard form by moving the decimal point to the left by the number equivalent to the exponent when the exponent is negative.

Explanation:

When asked what is 9.36×10-4 in standard form, we are being asked to convert a number from scientific notation to its regular number format. Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. To convert this to standard form, we move the decimal point to the left if the exponent is negative (or to the right if the exponent is positive) as many times as the value of the exponent.

In this case, we have a negative exponent (-4), so we move the decimal four places to the left:

9.36 -> 0.936 -> 0.0936 -> 0.00936 -> 0.000936

Therefore, 9.36×10-4 in standard form is 0.000936.

-7 = 7d - 8

Add 8 to both sides.

1 = 7d

Divide both sides by 7.

E. 168 sq units

The legs of this right triangle have length 24 and 14, so the area is ...

... A = (1/2)bh = (1/2)(24)(14) = 168 . . . . sq units

Answer:

[tex]y= \frac{1}{28} x^2[/tex]

Step-by-step explanation:

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

The pipe is located 7 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 7 inches from the vertex (0,0)

7 inches is the focus of the mirror

The distance between the vertex and the focus = 7

Since parabola is upwards and vertex is (0,0) we use formula

[tex]4py = x^2[/tex]

Where p is the distance between the vertex and focus

p = 7 we know

[tex]4*7*y = x^2[/tex]

[tex]28y = x^2[/tex]

Now isolate y by dividing 28 on both sides

[tex]y= \frac{1}{28} x^2[/tex]

Answer:

D) 75%

Step-by-step explanation:

75% of 24 = 0.75 x 24 = 18

Answer:

X = 37

Y = 29

Step-by-step explanation:

X + Y = 66

X - Y = 8

------

Solve second equation for X

X = Y + 8

Substitute for X in first equation

Y + 8 + Y = 66

2 * Y = 58

Y = 29

___

X - 29 = 8

X = 37

X = 37

Y = 29

Good Luck,

- I.A. -

Answer:

x = 37 and y = 29

Step-by-step explanation:

x + y = 66

x - y = 8

solve second equation for x

x = y + 8

substitute for x in first equation

y+8 +y = 66

2y = 58

y = 29

x - 29 = 8

x = 37

x = 37 and y = 29

Answer:

it should be 4x^3 y-4xy^2+xy+3x^2

Step-by-step explanation:

Answer:

x = 2/5

Step-by-step explanation:

[tex]x^3=\dfrac{0.008}{0.125}=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\\\x=\sqrt[3]{\dfrac{2^3}{5^3}}=\dfrac{\sqrt[3]{2^3}}{\sqrt[3]{5^3}}=\dfrac{2}{5}[/tex]

The value of x is 2/5.

Answer:

x = 2/5

Step-by-step explanation:

x^3 = .008/.125

Take the cubed root on each side

x^3 ^ (1/3)  = (.008/.125) ^ 1/3

Using ( a/b) ^c = a^c / b^c  and a^b^c = a^ (b*c)

x^(3 *(1/3))  = (.008) ^ 1/3 / (.125) ^ 1/3

x = (.008) ^ 1/3 / (.125) ^ 1/3

x = .2/.5

x = 2/5

600 m

The slope between 1 minute and 2 minutes is ...

... (800 -500)/(2 -1) = 300 . . . . . . m/min

Thus in 20 seconds, 1/3 minute, Jason will fall ...

... (1/3 min)·(300 m/min) = 100 m

This distance is in addition to the 500 m he has already fallen in the first minute.

In 1 min 20 sec, Jason falls 500 m + 100 m = 600 m.

_____

Comment on the graph

We don't expect Jason's rate of fall to change dramatically at the 2-minute mark. We suspect the last point should be (2 2/3, 1000).

Answer:

Step-by-step explanation:

Numerical reasoning

If all questions were 2-point, the total score would be 80. It is 20 more than that. Each 4-point question that replaces a 2-point question will add 2 points to the score, so there must be 20/2 = 10 of them.

There are 10 4-point questions and 30 2-point questions.

_____

With an equation

Let x represent the number of 4-point questions. Then 40-x is the number of 2-point questions. The total number of points is ...

... 2(40-x) +4x = 100

... 2x +80 = 100 . . . . simplify

... 2x = 20 . . . . . . . . .subtract 80

... x = 10 . . . . . . . . . . divide by 2.

There are 10 4-point questions and 40-10=30 2-point questions.

Answer:

(A) The number of bacteria is originally 300 and increases by 30% every hour

Step-by-step explanation:

I am assuming the function should actually read:

[tex]N(t)=300\cdot 1.30^t[/tex]

(i.e., there should be a "t" in the exponent. if this is not the case please disregard my answer).

According to the above exponential function, the initial amount 300 grows as (1+0.3)*300=300+0.3*300. In other words it increases by 30% every hour (t).

Your answer choice (A) is likely a candidate, except I am missing "every hour" at the end (again, am assuming this was omitted by mistake)

Final answer:

The function N(t)=300(1.30)^t represents the bacterial growth model where the initial amount of bacteria is 300 and increases by 30% every hour.

Explanation:

Looking at the function N(t)=300(1.30)^t, this model describes the number of bacteria, N, after t hours. The base number, 300, indicates the initial quantity of bacteria, while the term (1.30)^t suggests that the population changes by a factor of 1.30 each hour, reflecting a 30% increase in the number of bacteria each hour. Therefore, the correct statement that interprets this model is:

A. The number of bacteria is originally 300 and increases by 30% each hour.

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

[tex][x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}][/tex]

Let us substitute coordinates of point P and Q as:

[tex]x_1=-8[/tex],

[tex]y_1=-4[/tex]

[tex]x_2=4[/tex]

[tex]y_2=12[/tex]

[tex]m=3[/tex]

[tex]n=1[/tex]

[tex][x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}][/tex]

[tex][x=\frac{12-8}{4},y=\frac{36-4}{4}][/tex]

[tex][x=\frac{4}{4},y=\frac{32}{4}][/tex]

[tex][x=1,y=8][/tex]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

Answer:

Step-by-step explanation:

1,8

Answer:

Question 39: False

Question 43: True

Step-by-step explanation:

Question 39

|-4| is a solution of x ≤ 4

|-4| ⇒ This mean the absolute value of 4. The sign s are neglected.

So, |-4| is not a  solution of x ≤ 4.

Question 43

The point (5, -1) is a solution of the equation: y = 2x − 11.

To prove this we are to substitute the point (5, -1) in the equation y = 2x − 11.

y = -1 and x = 5

y = 2x − 11   ⇒   -1 = 2(5) -11

                         -1 = 10 - 11

                         -1 = -1

Answer:

7:10 (boys to girls)

10:7 (girls to boys)

7:17 (boys to everyone combined)

10:17 (girls to everyone combined)

~

Answer:

Each hiker gets [tex]\frac{7}{3}[/tex]  cups of mixed nuts.

Step-by-step explanation:

First, we need to find the total amount of cups by multiplying the number of bags with the amount of cups in each bag:

8 * 3.5 = 28

Now, we divide this by 12 to find the amount of cups per hiker:

28 ÷ 12 = [tex]\frac{7}{3}[/tex] or 2.3333

So each hiker gets  [tex]\frac{7}{3}[/tex]  cups of mixed nuts.

Answer:

42.5

Step-by-step explanation:

76.8% × ? = 32.64

? =

32.64 ÷ 76.8% =

32.64 ÷ (76.8 ÷ 100) =

(100 × 32.64) ÷ 76.8 =

3,264 ÷ 76.8 =

42.5

To solve for the number that 76.8% of it equals 32.64, you can write an equation and solve for x: 0.768 * x = 32.64. Dividing both sides by 0.768 gives x = 42.5.

The question asks about a percentage of a number, which is a math concept. If 76.8% of a number equals 32.64, you can use basic algebra to find that number. Let's call it 'x'. You can write it as an equation: 0.768 * x = 32.64. Solving for x, divide both sides of the equation by 0.768.

x = 32.64 /0.768

When you perform this calculation, you'll find that x is approximately 42.5. So, 76.8% of 42.5 is approximately 32.64.

https://brainly.com/question/32197511

#SPJ3

Answer:

Point

Step-by-step explanation:

If you are referring to geometry

Answer:

-1,81

Step-by-step explanation:

Multiplicity of a number can be written as power

for example

-1(multiplicity 3) can be written as

[tex]-1^{3}[/tex]= -1

similiarly 3(multiplicity 4) can be written as

[tex]3^{4}[/tex]=81

The eleventh-degree polynomial (x + 3)4(x – 2)7 has the same zeroes as did the quadratic, but in this case, the x = –3 solution has multiplicity 4 because the factor (x + 3) occurs four times (that is, the factor is raised to the fourth power) and the x = 2 solution has multiplicity 7 because the factor (x – 2) occurs ... Can you do the rest on your own?

Answer:

C. 1,-1

Step-by-step explanation:

The sum of the coefficient is 0 so x=1 is a root and (x-1) as a factor

so x^4+3x^3+3x^2-3X-4=(x-1)(x^3+4x^2+7x+4)

and the root of that is x=-1 and the factor is (x+1)

SO the answer is: x=1 and x=-1

Answer: -1, 1

Step-by-step explanation:

To solve the polynomial equation x^4 + 3x^3 + 3x^2 - 3x - 4 = 0, do a quick test of polynomials using 1 and -1 in place of x.

This gives the sum of coefficients as zero

Testing with 1: 1 + 3 + 3 - 3 - 4 = 0

Testing with -1: 1 + (-3) + 3 - (-3) - 4

= 1 - 3 + 3 + 3 - 4 = 0

This gives that both (x + 1) and (x - 1) are roots.

(x + 1)(x - 1) = x² - 1 {difference of two squares}

Dividing the polynomial x^4 + 3x^3 + 3x^2 - 3x - 4 by (x² - 1) results in x² - 3x + 4 as quotient. Factorizing this result would give complex roots.

Therefore, x² - 1 = 0

x² = 1

Taking square of both sides of the equation gives

x = ± 1

1 and -1 are the rational roots to the polynomial.

Answer:

f(x)= -x²-4x-2

Step-by-step explanation (this way is not the shortest one):

1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0

for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0

for the point (-1;1): a(-1)²+b(-1)+c=1

2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':

[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]

[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]

3. the required equation is: -x²-4x-2

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

_____

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer:

Probability that a vehicle is white, given that the vehicle is a car :

0.2222

Step-by-step explanation:

A: vehicle is white

probability that a vehicle is white =P(A)= 0.25

B:vehicle is a car

probability that it is a car =P(B)= 0.36

A∩B:vehicle is a white car

P(A∩B)=probability that it is a white car = 0.08

A/B:vehicle is white,given that vehicle is a car

to find P(A/B)

baye's theorem says that

P(A∩B)=P(A/B)×P(B)

⇒   0.08=P(A/B)×0.36

⇒  P(A/B)=0.2222

Hence, probability that a vehicle is white, given that the vehicle is a car is :

0.2222

Answer: 0.22

Step-by-step explanation:

confirmed