1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AleksandrR [38]
3 years ago
12

Find two consecutive whole numbers that square root 97 lies between

Mathematics
2 answers:
lora16 [44]3 years ago
8 0

Answer: 9 and 10

Step-by-step explanation:

To understand this question we need to first understand how to solve square root equations! The easiest way to learn how to solve square root problems is by finding the reverse of the problem.

For example, if you tried to find the square root of 25, you would reverse the problem to do 5^2 = 5 x 5 = 25.

So if we were to implement this problem, we would look at these two whole numbers.

9^2 = 9 x 9 = 81

10^2 = 10 x 10 = 100

Thus meaning that the only two numbers that the square root of 97 lies between can be 9 and 10!

It's important to rely on your knowledge of multiplication to develop a strong base for square roots.  

antoniya [11.8K]3 years ago
7 0

Answer:

9 & 10

Step-by-step explanation:

97 lies between two perfect squares, 81 and 100

Hence sqrt(97) would lie between sqrt(81) and sqrt(100), which are 9 and 10

You might be interested in
Which expression uses the associative property to make it easier to evalute?
mixas84 [53]

Answer:

The correct option is (c).

Step-by-step explanation:

The given expression is :

14(\dfrac{3}{2}\times \dfrac{1}{4})

We need to use the associative property to make it easier.

The associative property for multiplication is as follows :

A\times (B\times C)=(A\times B)\times C

We have,

A=14, B=\dfrac{3}{2}\ and\ C=\dfrac{1}{4}

14(\dfrac{3}{2}\times \dfrac{1}{4})=(14\times \dfrac{3}{2})\times \dfrac{1}{4}

Hence, the correct option is (c).

6 0
2 years ago
James spent $(2y2 + 6). He bought notebooks that each cost $(y2 − 1).
CaHeK987 [17]
The expression to find the number of notebooks James bought would be written as:

Number of notebooks = total spent / cost per item

Number of notebooks = (2y^2 + 6) / <span>(y^2 − 1)

</span><span>If y = 3, then the number of notebooks bought would be:

</span>Number of notebooks = (2y^2 + 6) / (y^2 − 1)
Number of notebooks = (2(3)^2 + 6) / (3^2 − 1)
Number of notebooks = 3 pieces<span>
</span><span>
</span>
7 0
3 years ago
Find sin(a)&amp;cos(B), tan(a)&amp;cot(B), and sec(a)&amp;csc(B).​
Reil [10]

Answer:

Part A) sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}

Part B) tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}

Part C) sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}

Step-by-step explanation:

Part A) Find sin(\alpha)\ and\ cos(\beta)

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

sin(\alpha)=cos(\beta)

Find the value of sin(\alpha) in the right triangle of the figure

sin(\alpha)=\frac{8}{14} ---> opposite side divided by the hypotenuse

simplify

sin(\alpha)=\frac{4}{7}

therefore

sin(\alpha)=\frac{4}{7}

cos(\beta)=\frac{4}{7}

Part B) Find tan(\alpha)\ and\ cot(\beta)

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

tan(\alpha)=cot(\beta)

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132

x=\sqrt{132}\ units

simplify

x=2\sqrt{33}\ units

Find the value of tan(\alpha) in the right triangle of the figure

tan(\alpha)=\frac{8}{2\sqrt{33}} ---> opposite side divided by the adjacent side angle alpha

simplify

tan(\alpha)=\frac{4}{\sqrt{33}}

therefore

tan(\alpha)=\frac{4}{\sqrt{33}}

tan(\beta)=\frac{4}{\sqrt{33}}

Part C) Find sec(\alpha)\ and\ csc(\beta)

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

sec(\alpha)=csc(\beta)

Find the value of sec(\alpha) in the right triangle of the figure

sec(\alpha)=\frac{1}{cos(\alpha)}

Find the value of cos(\alpha)

cos(\alpha)=\frac{2\sqrt{33}}{14} ---> adjacent side divided by the hypotenuse

simplify

cos(\alpha)=\frac{\sqrt{33}}{7}

therefore

sec(\alpha)=\frac{7}{\sqrt{33}}

csc(\beta)=\frac{7}{\sqrt{33}}

6 0
3 years ago
Which expression is equivalent to the following complex fraction?
sasho [114]

Answer: (D) \frac{y-x}{y+x}

Explanation:

\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}=\frac{\frac{y-x}{xy}}{\frac{y+x}{xy}}=\frac{y-x}{y+x}

Just a note on writing down these expressions: I recommend using parentheses whenever you can to avoid misinterpretation. An expression 1/x-1/y / 1/x+1/y could be interpreted by someone as 1/x-(1/y / 1/x)+1/y, which is a different thing.

6 0
3 years ago
Read 2 more answers
Surface area of a sphere. Please help and no links please.
V125BC [204]

Answer:

725.4656 - surface area

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Suppose that the amount of time one spends in a bank is exponentially distributed with an average frequency of 6 customers per h
    5·1 answer
  • Determine the standard form of the equation of the line that passes through (-7 8) and (0 -8)
    8·2 answers
  • Using the equation y=4x+19 and h=3x+25, whatv is the value of y when x is 4?
    7·1 answer
  • Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
    6·1 answer
  • Luis put out 6 different pies at a picnic at the end of the picnic, he noticed this about the pies: one whole apple pie was eate
    9·1 answer
  • 7. (2x - 1)2 = 31 – 2x<br> solve by factoring
    13·1 answer
  • 14. Ashton has 3 less dollars than Cole. This relationship can be represented by an equation using
    6·1 answer
  • Please help, sorry the image is blurry I retook it multiple times.
    12·1 answer
  • Help please :,))))))
    12·1 answer
  • The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph,
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!