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3 years ago

2 ways to decompose the number 749

Mathematics

1 answer:

kolezko [41]3 years ago

6 0

Okay. You can decompose 749 with these ways:
700 + 40 + 9
or
500 + 200 + 40 + 9

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Which is the equation of a line that passes through the point (3.-4

gtnhenbr [62]

Answer:B

Step-by-step explanation:

A. y = 2x-11

B. y = 2x-10

c. y = 2x-4

D. y=2x-2

Recall, the slope intercept equation

y= mx+c

Assuming c is held constant in each scenario

Looking at A

m = 2, c = -11

Equation of the line that passes through the point (3.-4)

-4 = 2×3 + c

c =-10

-10 does not correspond to -11 given

Let's try B

m= 2, c = -10

Equation of the line that passes through the point (3.-4)

-4 = 2×3 + c

c = -4-6 = -10

This intercept correspond with the intercept in B which is -10

Let's look at C

m= 2, c = -4

Equation of the line that passes through the point (3.-4)

-4 = 2×3 + c

c = -4-6 = -10

-10 does not correspond to -4 given

Let's try D

m= 2, c = -2

Equation of the line that passes through the point (3.-4)

-4 = 2×3 + c

c = -4-6 = -10

-10 does not correspond to -2 given

7 0

3 years ago

The gas tank of a riding mower holds 5 liters of gas.How many 5 -liters gas tanks can you fill from a full 20- liter gad can?

aliina [53]

Answer:

Step-by-step explanation:

If the gas tank holds 5 liters and you have 20 liters, then 20/5 = 4 times it will fill it up.

8 0

3 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

5 0

3 years ago

Identify the type of conic section that has the equation 9x2+ 16y2 = 144 and identify its domain and range.

Kobotan [32]

9 x² + 16 y² = 144 /:144
$\frac{ x^{2} }{16} + \frac{ y^{2} }{9} =1$
General formula of ellipse ( the center is at the origin ): $\frac{ x^{2} }{ a^{2} }+ \frac{ y^{2} }{ b^{2} } =1$
a² = 16, b² = 9
Domain: [-a, a ] = [-4, 4]
Range:[-b, b ]
Answer: B ) ellipse.
Domain: { -4 ≤ x ≤ 4 }
Range: { -3 ≤ y ≤ 3 }

8 0

3 years ago

Help! What does 2 divided by 9 tenths

Serga [27]

I got 0.45

Good luck!

6 0

3 years ago

Read 2 more answers