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3 years ago

For the figure below, circle the statement that must be true

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

Therefore the true statement is option b . SK > YU

Step-by-step explanation:

Given:

SA ≅ OY

AK ≅ OU

∠A = 90°

∠O = 70°

To Prove:

SK > YU

Proof:

We have,

Hinge theorem:

States that ''if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle''.

In Δ SAK and Δ YOU

SA ≅ OY

AK ≅ OU

∠ A is larger than ∠O

i.e 90 > 70

Side opposite to 90 > Side opposite to 70

∴ SK > YU ..............Proved

Therefore the true statement is option b . SK > YU

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Please help me! And please no scam answers

Yuri [45]

Answer:

Average rate of change: $-3$

Step-by-step explanation:

Remember:

The average rate of change of a function over an interval $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$

Given:

$[a,b]=[1,7]$

$f(b)=f(7)$

$f(a)=f(1)$

Calculation:

$f(b)=f(7)=-(7)^2+5(7)+14=-49+35+14=-49+49=0$

$f(a)=f(1)=-(1)^2+5(1)+14=-1+5+14=4+14=18$

$\frac{f(b)-f(a)}{b-a}=\frac{0-18}{7-1}=\frac{-18}{6}=-3$

Therefore, the average rate of change of the function $g(x)=-x^2+5x+14$ over the interval $1\leq x\leq7$ is $-3$ .

6 0

3 years ago

What is the sum of the first 37 terms of the arithmetic sequence?

lidiya [134]

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

The sum of the first n terms of an arithmetic sequence is given by:

$S_{n} = \frac{n(a_{1} + a_{n})}{2}$

In this question:

$a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6$

We want the sum of the first 37 terms, so we have to find $a_{37}$

$a_{n} = a_{1} + (n-1)*d$

$a_{37} = a_{1} + (36)*d$

$a_{37} = -27 + 36*6$

$a_{37} = 189$

Then

$S_{37} = \frac{37(-27 + 189)}{2} = 2997$

The sum of the first 37 terms of the arithmetic sequence is 2997.

6 0

3 years ago

27 divided by 52,758

marta [7]

Answer:

511

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

a graphic designer wants to know the number of regions that are formed when circles overlap in particular. can she find a rule t

kumpel [21]

Answer:

A. 2

Step-by-step explanation:

Its successive multiples and it increases:

+2, +4, +6, +8

it increases by 2 every time which is successive multiples so the answer is A, 2.

3 0

3 years ago

According to the rational root theorem, which of the following are possible

White raven [17]

Given:

The polynomial function is

$F(x)=4x^3-6x^2+9x+10$

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of $\dfrac{p}{q}$ , where, p is a factor of constant and q is the factor of leading coefficient.

We have,

$F(x)=4x^3-6x^2+9x+10$

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

$x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}$

Therefore, the correct options are A, C, D, F.

7 0

3 years ago