MATHEMATICS HIGH SCHOOL

Solve the system using the method of your choice: y = 3x – 4 2x + 4y = 26 SHOW WORK

Answers

Answer 1

Answer:

Hello Savanna

y=3x-4

2x+4y=26

Can we solve it together ? :) Thx

We need to solve y=3x-4 for y

Now let's start solving this by substitute 3x-4 for y in 2x+4y=26

2x+4(3x-4)=26

14x-16=26

Now let's add 16 to both sides

14x-16+16=26+16

14x=42

Divide both sides by 14 so we can find the value for x

14x/14= 42/14

x=3

Good job:) now we find the value of x

We are not done yet.

Let's find the value for y by substitute 3 for x in y=3x-4

y=3x-4

y=(3)(3)-4

y=9-4

y=5

Yeah well done :)

Final answer : x=3 and y=5

(3,5)

Was that helped ? please rate my answer :0

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Determine the remainder when (5x3 + 49x2 + 74x + 6) is divided by (x + 8).

1089
141°
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Answers

Answer:

The answer is that x is equal to 33⁰

Jayden’s new puppy weighed 11 and one fourth pounds at 4 weeks old. At four weeks, the puppy weighed three fifths times as much as at 16 weeks. Which equation can be used to find how much Jayden’s puppy weighs at 16 weeks old

Answers

Step-by-step explanation:

Weight of the puppy at 4 weeks old:

$\large{11 (1)/(4) }$ pounds = $\large{ (45)/(4) }$ pounds

This weight is 3/5th times of the weight of puppy in 16 weeks. Let's assume the weight of puppy in 16 weeks be x. Then, 3/5th of x is 45/4 pounds.

Inequationform,

$\boxed{ \large{(3)/(5) x = (45)/(4) }}$

Multiplying 5/3 both sides to isolate x on LHS,

$\large{x = (45)/(4) * (5)/(3) }$

$\large{x = (75)/(4) = 18.75}$ pounds

The equation used for finding the weight of puppy is 3x/5 = 45/4. And Jayden's puppy weighed 18.75 pounds in 16 weeks.

Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function?

Answers

Answer
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98
=9.8×10⁻¹

Explanation
The investment of $10,000 decreases by 2% every year. So the following year is usually (100 - 2)=98% of the previous year. This is a geometric progression.
In this case the first term = 10000
The second term = 98% × 10000 = 9800.
The common ratio = 9800/10000=49/50
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98.
The equation of the exponential rate would be;
10,000ₓ0.98ⁿ.
where n is the number years.

Answer: B

Step-by-step explanation:

0.98

E2020

a 60 foot cable is stretched from the top of a pole to an anchor it is anchored on the ground 19 feet away from the base of the pole how tall is the pole

Answers

Answer:

56.95 feet

Step-by-step explanation:

To find the height of the pole, you can use the Pythagorean Theorem because the cable, the height of the pole, and the distance from the base of the pole to the anchor form a right triangle.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side).

In this case, the height of the pole is the side we want to find (let's call it "h"), the distance from the base of the pole to the anchor is 19 feet (let's call it "d"), and the cable's length is 60 feet (the hypotenuse).

So, the equation is:

h^2 + d^2 = hypotenuse^2

h^2 + 19^2 = 60^2

Now, we can solve for "h":

h^2 + 361 = 3600

Subtract 361 from both sides:

h^2 = 3600 - 361

h^2 = 3239

Now, take the square root of both sides to find "h":

h = √3239

h ≈ 56.95 feet

So, the height of the pole is approximately 56.95 feet.

1. For which value of x is the expression log base 4 of (x+3) not defined?a. 0
b. -2
c. 3
d. -4

2. If log 7= a, what is the value of log 490 in terms of a?

3. For what value of k will the graph of y=log base 7 of x contain the point (1,k)?

Answers

1.
$log_a b \na>0 \hbox{ and } a \not=1 \nb>0 \n \nlog_4 (x+3) \nx+3>0 \nx>-3$

log₄(x+3) is defined for x greater than -3.
0>-3
-2>-3
3>-3
4≤-3
The answer is D. -4.

2.
$\log 7=a \n \n\log 490= \log (7^2 \cdot 10)=\log 7^2 + \log10=2 \log 7 + 1=2a+1$

The formulas I used:
$\log_a (x \cdot y)=\log_a x + \log_a y \n\log_a x^y=y \log_a x \n\log x=\log_(10) x$

3.
$y=\log_7 x \n \n(1,k) \nx=1 \n y=k \n \nk=\log_7 1 \nk=\log_7 7^0 \nk=0$

Which represents a quadratic function?f(x) = −8x3 − 16x2 − 4x

f (x) = x 2 + 2x − 5

f(x) = + 1

f(x) = 0x2 − 9x + 7

Answers

A quadratic function is one of the form f(x) = ax^2 + bx + c, where a, b, and c are numbers with a not equal to zero. In the given question, the only function that satisfies the condition of a quadratic function is f(x) = x^2 + 2x - 5 and thus is the correct answer to the question.

Answer:

f (x) = 3/4 x ^2 + 2x − 5

Step-by-step explanation:

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