MATHEMATICS HIGH SCHOOL

Enter the correct value so that each expression is a perfect-square trinomial.x2 – 10x +_____

Answers

Answer 1

Answer:

Answer:

A = 25 so that the expression $x^2-10x+A$ is a perfect-square trinomial.

Step-by-step explanation:

Given : expression $x^2-10x+A$

We have to find the value of A so that each expression is a perfect-square trinomial.

perfect-square is the term in the form of $(a+b)^2 \ or\ (a-b)^2$

Since , we know the algebraic identity,

$(a+b)^2=a^2+b^2+2ab\n\n (a-b)^2=a^2+b^2-2ab$

Given expression $x^2-10x+A$ is of the form of $(a-b)^2=a^2+b^2-2ab$

Thus, comparing , we get,

a= x ,

-2ab = -10x

⇒ b = 5

Thus adding b² term to get perfect-square trinomial.

b² = 25

Thus, the perfect-square trinomial becomes $x^2-10x+25=(x-5)^2$

So, A = 25

Answer 2

Answer: the answer is x2-10x+25 because that is half of -10 (5) squared

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Use the substitution method to solve the system of equations

3x+2y=13

y=x-1

Answers

Answer:

$x=3\ny=2$

Step-by-step explanation:

$3x+2y=13\ny=x-1$

Solve for $y=x-1$ for y:

$y=x-1$

Substitute $x-1$ for y in $3x+2y=13$ :

$3x+2y=13$

$3x+2(x-1)=13\n$

$5x-2=13$

$5x=13+2$

$5x=15$

$x=15/5$

$x=3$

Substitute 3 for x in $y=x-1$ :

$y=x-1$

$y=(3)-1$

$y=2$

$x=3$ and $y=2$

hope this helps...

What is the next odd number after 160 to which 9 would divide without a reminder

Answers

ok so one way is to list the multiplues of 9 close to thtat
first use a caltulator to find out how much more we need
160/9=17.777777
that is 17.7777 nine's
so round up
18
18 is even
odd times even=even
18 must be odd
18+1=19
9 times 19=171
the answer is 171

160 divided by 9 is 17.78. 9 goes into 162 but that is even. The next number 9 goes into is 171 and that is odd so the. answer is 171.

A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. The area A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 90°, what is the area of the opening?

Answers

We are already given with the function to solve for the area:
A(θ) = 16 sin θ ⋅ (cos θ + 1)

We simply have to substitute the value of the angle into the function. So,
If θ = 90°,
A(90°) = 16 sin (90°) ( cos (90°) + 1 )

Using the calculator or the definition of trigonometric functions at angle of 90°, we get the value of the area:
A(90°) = 16 square inches

we know that

The area A of the opening may be expressed as the function:

$A(\alpha) = 16 sin \alpha* (cos \alpha + 1)$

For $\alpha =90$ °

We simply have to substitute the value of the angle into the function

$A(90) = 16*sin 90* (cos 90 + 1)$

$A(90) = 16*(1)* (0 + 1)$

$A(90) = 16 in^(2)$

therefore

the answer is

the area of the opening is $16 in^(2)$

Briyana has $150, and she needs to save at least $560 for a spring break trip. If she can save $45 per week, how long will it take her to save enough money? Let w = weeks saving money. Write an inequality to describe the situation.

45w + 150< 560

45w + 150> 560

150w + 45< 560

150w + 45 > 560

Answers

Answer: The answer is (B)

45w + 150> 560.

Step-by-step explanation: Given that 'w' represents the number of weeks s

Briyana saves money.

Since she can save $45 per week, so the amount of money she can save in 'w' weeks is $45w.

Also, she has $150 already with her, so the total amount of money saved is given by (45w + 150).

Now, since she needs to save at least $560, so we must have

45w + 150 > 560.

Thus, (B) is the correct option.

Answer:

Step-by-step explanation:

suppose a sorority sells 500 raffle tickets to raise money for a local charity. you purchase 17 of the tickets. if the winning ticket is chosen at random, what is the probability that one of your tickets is chosen as the winning ticket?

Answers

if you have 17 of the 500 tickets, the probability one of yours will be picked is $(17)/(500)$

Find the slope and y intercept
y=2

Answers

y = 0x + 2

Slope = 0

Y-intercept = 2

The line is parallel to the x-axis,
so there is no x-intercept.

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