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2 years ago

Prove that MNQ is congruent to PNQ (URGENT) help with all blanks

Mathematics

1 answer:

katrin2010 [14]2 years ago

4 0

Answer:

In triangle QNP and QNM

3.QN=QN[common side]

so triangle QNP and QNM is CONGRUENT by A.A .S axiom.

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Could someone help me? solve for x

Molodets [167]

$5x+2 =42 \\\\$

minus 2 each side.

$5x=40$

then divide

$x=8$

6 0

2 years ago

State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli

nasty-shy [4]

Answer:

Part A

$f(n)=52-12(n-1)$

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$ Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right$

Part D:

$h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right$

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

$(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12$

Explicit Formula

To write an explicit formula is to write it as function.

$f(n)=52-12(n-1)$

Recursive Formula

To write it as recursive formula, is to write it as recurrence given to some restrictions:

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

$(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\$

Arithmetic Sequence, difference

$d=\frac{2}{4}$

Explicit Formula:

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)$

Recursive Formula

$g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.$

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

Explicit formula

$h(n)=1.1+0.4(n-1)\\$

Recursive Formula

$h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.$

6 0

3 years ago

Help me please by solving and showing the steps:)

Lorico [155]

Answer:

$-\frac{3\sqrt[3]{t} }{2}$

Step-by-step explanation:

1: Write g(t) as y, resulting in $y=-\frac{8}{27}t^3$

2: Interchange the variables y and t, resulting in $t=-\frac{8}{27}y^3$

3: Multiply both sides by 27, resulting in $27t=-8y^3$

4: Divide both sides by -8, resulting in $-\frac{27t}{8}=y^3$

5: Find the cube root of both sides, resulting in $\sqrt[3]{-\frac{27t}{8} }=y$

6: Apply a radical rule, resulting in $-\sqrt[3]{\frac{27t}{8} } =y$

7: Apply another radical rule, resulting in $-\frac{\sqrt[3]{27t} }{\sqrt[3]{8} } =y$

8: Simplify the denominator, resulting in $-\frac{\sqrt[3]{27t} }{2} =y$

9: Apply yet another radical rule, resulting in $-\frac{\sqrt[3]{27}\sqrt[3]{t} }{2} =y$

10: Simplify $\sqrt[3]{27}$ , resulting in $-\frac{3\sqrt[3]{t} }{2} =y$

3 0

2 years ago

The supplement of an angle is four times the complement of the angle find the measure of the complement

Morgarella [4.7K]

Answer:

The measure of the complement is 30°

Step-by-step explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

Two angles are complementary if their sum is equal to 90 degrees

Let

x -----> the measure of an angle

we know that

180°-x=4(90°-x)

Solve for x

180°-x=360°-4x

4x-x=360°-180°

3x=180°

x=60°

Find the complement

90°-x=90°-60°=30°

8 0

2 years ago

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if you divide a five-digit number by a one-digit number, what is the largest possible remainder you can get ?

solmaris [256]

99999/8 has a remainder of 7

6 0

3 years ago

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