Solve for x. fraction numerator x plus 5 over denominator 4 end fraction equals fraction numerator 2 x plus 1 over denominator 2 end fraction

The correct equation that represents the direct variation between the total cost of gasoline and the number of gallons purchased is C = 1.46n.

The question involves finding the equation that represents the direct variation between the total cost of gasoline c, and the number of gallons purchased n. Kathy pays $23.36 for 16 gallons of gasoline. To find the unit price, we divide the total cost by the number of gallons:

$23.36 ÷ 16 gallons = $1.46 per gallon

Since the total cost varies directly with the number of gallons, we can express this as c = $1.46 × n. Thus, option A, C = 1.46n, shows the correct relationship between the total cost of gasoline, c, and the number of gallons purchased, n.

Answer:

3/4 *7= 3/4 * 7/1=21/4=5 1/4

Step-by-step explanation:

Answer:

The addition of given fractions is [tex]\frac{11}{12}[/tex]

Therefore [tex]\frac{1}{4}+\frac{2}{3}=\frac{11}{12}[/tex]

Step-by-step explanation:

Given fractional expression is [tex]\frac{1}{4}+\frac{2}{3}[/tex]

To find the addition of given fractions :

Adding the given fractions we get

[tex]\frac{1}{4}+\frac{2}{3}[/tex]

[tex]=\frac{1(3)+2(4)}{12}[/tex] ( here taking 12 as LCM )

[tex]=\frac{3+8}{12}[/tex]

[tex]=\frac{11}{12}[/tex]

Therefore [tex]\frac{1}{4}+\frac{2}{3}=\frac{11}{12}[/tex]

The addition of given fractions is [tex]\frac{11}{12}[/tex]

Answer: i think 4x4/8

Step-by-step explanation:

Answer:first one

Step-by-step explanation:4 2/8

Just watched like 3 vids on multiplying unit fractions by whole numbers

Answer: First option.

Step-by-step explanation:

Below are some transformations for a function [tex]f(x)[/tex]:

1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.

2 If [tex]f(x)-k[/tex], the function is shifted "k" units down.

3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.

4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.

5. If [tex]-f(x)[/tex], the function is reflected over the x-axis.

6. If [tex]f(-x)[/tex], the function is reflected over the y-axis.

Then, given the parent function [tex]f(x)[/tex]:

[tex]f(x)=2^x[/tex]

And knowing that the the other function is:

[tex]g(x)=-2^{(x+4)}-2[/tex]

You can identify that the function [tex]g(x)[/tex] is obtained by:

- Shifting the function [tex]f(x)[/tex] 4 units left.

-  Reflecting the function  [tex]f(x)[/tex] 4 over the x-axis.

- Shifting the function [tex]f(x)[/tex] 2 units down.

Answer:

A is correct

Step-by-step explanation:

Answer: 3%

Step-by-step explanation:

S.I = ptr / 100

Interest = 4515 - 4500

Interest = 15

time = 4 months = 4/12 years = 1/3 years

substituting each value into the equation to find rate , we have

15 = 4500 x  1/3 x r  / 100

1500 = 4500 x 1/3 x r

3(4500) = 4500r

r = 3(4500) / 4500

r = 3%

Answer:

3

Step-by-step explanation:

the guy is right above me

The location of point A of the number line will be at 2 ¹/₃.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The section between the numbers 2 and 3 will be 3.

The location of point A is given as,

⇒ 2 + 1/3

Convert the expression into a mixed fraction number. Then we have

⇒ 2 + 1/3

⇒ 2 ¹/₃

The location of point A of the number line will be at 2 ¹/₃.

More about the number line link is given below.

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Answer:

I dont know what they tought you in your school...but pizza is 100% good, and 8/2 is 8divided by2 so the answer is 4.

PLESASE MART BRAINLIEST. IT'S OK IF NOT BUT STILL THX.

Answer:

pizza is very good and 8/2 is 4.

Step-by-step explanation:

pls mark brainliest thx! :)

Answer:

d

Step-by-step explanation:

Answer:

The answer is D: 1,456

Step-by-step explanation:

I got it right on edge

Answer:

Step-by-step explanation:

y=0.23x+1

f(2)=0.23(2)+1=0.46+1=1.46

f(0)=0.23(0)+1=0+1=1

f(-3)=0.23(-3)+1=-0.69+1=0.31

39 miles ------------------------------------------------

Answer:

Yes, it is a rectangle

Step-by-step explanation:

12 ^2 +35^2 =37^2

Answer:

73

Step-by-step explanation:

Answer:

To do this you want to plug 3 in for d, so your equation will look like this

7(3)^2+10

In the order of PEMDAS you want to do exponents first, because there is no parentheses.

7*9+10 (3^2=9), next you want to multiply

63+10, lastly you want to add

63+10=73

73

Hope this helps ;)

Step-by-step explanation:

A(promotional sign)b

A=kb

4=21k

K=0. 1904

A=0. 2b

A=0. 2×7

A=1. 4

:

Step-by-step explanation:

a varies directly with b

a ∞ b

a = Kb

K is the constant of proportionality

If a = 4 when b = 21

4 = 21×k

4 = 21k

k = 4/21

: - a = 4b/21

find a when b= 7.

a = 4(7)/21

a = 4/3

a = 1 1/3

Answer:

3/4 book per month

Step-by-step explanation:

12/16=3/4

Ashley's reading rate is calculated by dividing the total number of books she read (12 books) by the number of months it took her to read them (16 months), which gives 0.75 book per month.

The question is about determining Ashley's rate of reading in terms of books per month. The rate is determined by dividing the total number of books she has read by the total number of months. In this case, Ashley has read 12 books in 16 months.

To find Ashley's reading rate, you would divide the total number of books she has read (12 books) by the number of months it took her to read them (16 months), that is 12 books ÷ 16 months = 0.75 book per month.

So Ashley's reading rate is 0.75 book per month.

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Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{1}{4}[/tex] and c = - 1, thus

y = [tex]\frac{1}{4}[/tex] x - 1 → C

Answer:

Given that AC ≅ BC, the sides are of equal measures.

CD is a side in both ΔACD and ΔBCD, so the side is equal in both triangles.

Given that CD if the bisector of ∠ACB, the two angles produced are equal: ∠ACD ≅ ∠BCD.

∠ACB is contained between AC and CD in ΔACD. ∠ACB is contained between BC and CD in ΔBCD.

Therefore by the SAS postulate, ΔACD ≅ ΔBCD.

Step-by-step explanation:

The SAS postulate says that if two triangles have a contained angle between two sides that are known to be equal in the other triangle, then the triangles are congruent.

Prove that two sides are equal, then prove that an angle that is between those two sides is also equal.

Answer:

Step-by-step explanation:

6x + 7zy = 15

7zy = 15-6x

y = (15-6x)/7z

Answer:

(-1,5)

Step-by-step explanation:

Let the coordinates of point A be (a,b).

We have that B is at (-5,1)

Assuming M(-3,3) is the midpoint of the segment AB, then

[tex](-3, 3 )= ( \frac{a + - 5}{2}, \frac{b + 1}{2} )[/tex]

This means that:

[tex]- 3 = \frac{a + - 5}{2}[/tex]

and

[tex]3 =\frac{b + 1}{2}[/tex]

This implies that 2*-3=a-5 and 3*2=b+1

-6=a-5 and 6=b+1.

a=5-6 and b=6-1

a=-1 and b=5.

Therefore the coordinates of A are:

(-1,5)

Answer:

37

Step-by-step explanation:

Plug 5 in for b .

7.4 * 5 = 37

Answer:

Step-by-step explanation:

Amount the teacher as $400

A calculator cost $70

The no. Of calculator he teacher can get is = 400/70 = 5.71

The teacher can get 5 calculator

The population of bacteria after 40 hours is 254

Step-by-step explanation:

Initial population of bacteria = 40

Growth rate: Doubles every 15 hours

The population function is given as:

[tex]P_t = P_0 * r^t[/tex]

Here

P0 is the initial population

r is the growth rate

and t is the time in hours

The growth rate will be: [tex]2^{\frac{t}{15}}[/tex]

Putting the values in the function

[tex]P_t = 40 * 2^{\frac{40}{15}}\\P_t = 40 * 2^{2.67}\\P_t = 40 * 6.34960...\\P_t = 253.98416...[/tex]

Rounding off to nearest whole number we get

P_t ≅254

Keywords: Population growth,, bacteria

Learn more about population growth at:

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From the information, the population of the bacteria will be 254.

Based on the information given, the population function will be:

= P × 2r

where, P = initial population of the bacteria

= 40 × 6.349

= 253.98

= 254

Therefore, it can be deduced that the population of the bacteria after 4 hours will be 254.

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Answer:

8 pizzas can serve 16 guests.

Step-by-step explanation:

So the caterer usually prepares 4 pizzas, but now she prepared twice as many, which means that now there are 4 • 2 = 8 pizzas.

Also, there is an estimation that each guest will eat 1/2 of a pizza.

In order to answer how many guests will 8 pizzas serve, we need to write an equation (pizzas per guest multiplied with number of guests equals the number of pizzas). Let's mark the unknown number of guests with x:

1/2 • x = 8

x = 8 / 1/2

x = 16

So, if each guest eats 1/2 of a pizza, then 8 pizzas will be enough to serve 16 guests.

Answer:

Therefore the answer is the fourth option y = f(x) = [tex]x^{2}[/tex]  - 8x + 13

Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.

Step-by-step explanation:

i) f(x) = [tex]x^{2}[/tex] + 8x + 19    =  [tex](x + 4)^{2}[/tex] + 3. SO the vertex is at (-4, 3)

Therefore the answer is the fourth option y = f(x) = [tex]x^{2}[/tex]  - 8x + 13

 = ([tex]x^{2}[/tex]  - 8x + 16) + 3  = [tex](x-4)^{2}[/tex] - 3

Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.

Final answer:

The function with a vertex at the point (4, -3) is f(x) = x² - 8x + 13. This is concluded by using the vertex formula for a quadratic equation and checking the resulting coordinates against the given options.

Explanation:

The question is asking which of the given functions has a vertex at the point (4, -3). To find the vertex of a quadratic function of the form f(x) = ax² + bx + c, we can use the vertex formula, which is h = -b/(2a) for the x-coordinate, and then plug that back into the equation to find the y-coordinate. In this case, the function with the vertex (4, -3) must have the x-coordinate of the vertex at x = 4. Plugging this into the vertex formula, we get 4 = -b/(2a). We then look for a function where -b/(2a) = 4. The function f(x) = x² - 8x + 13 is the correct one because when we apply the formula -(-8)/(2*1) = 8/2 = 4. To confirm, we substitute x = 4 into the function: (4)² - 8(4) + 13 = 16 - 32 + 13 = -3, which gives us the y-coordinate of the vertex, -3.

Answer: 19/4

Explanation: To write a mixed number as an improper fraction, first multiply the denominator times the whole number and then add the numerator.

So here, we multiply the denominator which is 2 times the whole number, 3, and then we add the numerator. So we have (4 x 4) + 3 which simplifies to 19.

Finally, we put our new number over our old denominator and we have our answer which is 19/4.

So 4 and 3/4 can be rewritten as the improper fraction 19/4.

Explanation of converting [tex]4\frac{3}{4}[/tex] to an improper fraction as 19/4.

To convert the mixed number  [tex]4\frac{3}{4}[/tex]  to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator:

4 x 4 + 3 = 19

So,  [tex]4\frac{3}{4}[/tex]  as an improper fraction is 19/4.

Answer:

17

Step-by-step explanation:

Given:

The given expression is.

[tex]3x+2[/tex]

We need to solve the given expression for [tex]x = 5[/tex].

Solution:

Rewrite the expression as.

[tex]f(x)=3x+2[/tex]

Substitute x = 5 in above expression.

[tex]f(5)=3(5)+2[/tex]

[tex]f(5)=3\times 5 + 2[/tex]

Now we multiply 5 with 3.

[tex]f(5)=15+2[/tex]

Now we add right side terms.

[tex]f(5)=17[/tex]

Therefore, The correct value of given expression is [tex]3x+2=17[/tex] for [tex]x=5[/tex].

Answer:

2x + 5y = - 15

Step-by-step explanation:

The line that passes through (–5, –1) and (10, –7) points and the point-slope form of the equation is [tex]y + 7 = - \frac{2}{5}(x - 10)[/tex].

Now, we have to arrange this in the standard form.

So, [tex]y + 7 = - \frac{2}{5}(x - 10)[/tex]

⇒ 5(y + 7) = - 2(x - 10)

⇒ 5y + 35 = - 2x + 20

⇒ 2x + 5y = - 15 (Answer)