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3 years ago

14

Classify the system and determine the number of solutions. Check all that apply. {7x + y = 13 28x + 4y = -12 A) inconsistent B

)consistent C)infinitely many solution D) no solution

1 answer:

Ostrovityanka [42]3 years ago

4 0

$\left\{\begin{array}{ccc}7x+y=13&|multiply\ both\ sides\ by\ (-4)\\28x+4y=-12\end{array}\right\\+\left\{\begin{array}{ccc}-28x-4y=-52\\28x+4y=-12\end{array}\right\ \ \ |add\ the\ sides\ of\ the\ equations\\------------\\.\ \ \ \ \ \ \ \ 0=-64-FALSE\\\\Answer:A)\ inconsistent\ and\ D)\ no\ solution.$

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Please help me with this

mash [69]

Answer:

The correct answer is first option

24

Step-by-step explanation:

From the figure we get, mAXM = 72° and m<AMR = 38°

Also it is given that, all triangles are isosceles triangles and

m<FXA = 96°

<u>To find the measure of <FXM</u>

From the figure we get,

m<FXA = m<AXM + m<FXM

m<FXM = m<FXA - m<AXM

= 96 - 72

= 24

Therefore the correct answer is first option

24

4 0

3 years ago

If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),

nikklg [1K]

Step-by-step explanation:

<u>Step 1: Solve using the first point</u>

<em>(2, 28)</em>

$28 = a(2)^3 + b(2)^2 + c(2) + d$

$28 = 8a + 4b + 2c + d$

<u>Step 2: Solve using the second point</u>

<em>(-1, -5)</em>

$-5 = a(-1)^3 + b(-1)^2 + c(-1) + d$

$-5 = -a + b - c + d$

<u>Step 3: Solve using the third point</u>

<em>(4, 220)</em>

$220 = a(4)^3 + b(4)^2 + c(4) + d$

$220 = 64a + 16b + 4c + d$

<u>Step 4: Solve using the fourth point</u>

<em>(-2, -20)</em>

$-20 = a(-2)^3 + b(-2)^2 + c(-2) + d$

$-20 = -8a + 4b - 2c + d$

<u>Step 5: Combine the first and fourth equations</u>

<u /> $28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d$

$8 = 8b + 2d$

$8 - 8b = 8b - 8b + 2d$

$(8 -8b)/2 = 2d/2$

$4 - 4b = d$

<u>Step 6: Solve for c in the second equation</u>

$-5 + 5 = -a + b - c + d + 5$

$0 + c = -a + b - c + c + d + 5$

$c = -a + b + d + 5$

<u>Step 7: Substitute d with the stuff we got in step 5</u>

$c = -a + b + (4 - 4b) + 5$

$c = -a + b + 4 - 4b + 5$

$c = -a - 3b + 9$

<u>Step 8: Substitute d and c into the first equation</u>

<u /> $28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)$

$28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b$

$28 - 22 = 6a - 6b + 22 - 22$

$6 / 6 = (6a - 6b) / 6$

$1 + b = a - b + b$

$1 + b = a$

<u>Step 9: Substitute a, b, and c into the third equation</u>

$220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)$

$220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b$

$220 - 100 = 60b + 100 - 100$

$120 / 60 = 60b / 60$

$2 = b$

<u>Step 10: Find a using b = 2</u>

$a = b + 1$

$a = (2) + 1$

$a = 3$

<u>Step 11: Find c using a = 3 and b = 2</u>

$c = -a - 3b + 9$

$c = -(3) - 3(2) + 9$

$c = -3 - 6 + 9$

$c = 0$

<u>Step 12: Find d using b = 2</u>

$d = 4 - 4b$

$d = 4 - 4(2)$

$d = 4 - 8$

$d = -4$

Answer: $a = 3, b = 2, c = 0,d = -4$

6 0

2 years ago

Read 2 more answers

the density of a certain material is such that weighs 6900 grams for every 4.5 quarts of volume express this density in pounds p

dlinn [17]

Answer:

$d=101.4\ \text{pounds}/\text{feet}^3$

Step-by-step explanation:

Given that,

Mass of material, m = 6900 grams

Volume of the material, V = 4.5 quarts

We need to find the density in pounds per cubic foot

We know that,

1 pound = 453.59 grams

⇒ 6900 grams = 15.21 pounds

Also, 1 cubic foot = 29.92 quarts

4.5 quart = 0.15 feet³

Density = mass/volume

Or

$d=\dfrac{15.21\ \text{pounds}}{0.15\ \text{feet}^3}\\\\d=101.4\ \text{pounds}/\text{feet}^3$

Hence, the density of the material is $101.4\ \text{pounds}/\text{feet}^3$

3 0

3 years ago

Find the slope of the line y = 1/6x + 3/2

AURORKA [14]

Answer: 1/6

Step-by-step explanation:

Slope is the m in y=mx+b

7 0

2 years ago

Read 2 more answers

If $x$, $y$, and $z$ are positive integers such that $6xyz+30xy+21xz+2yz+105x+10y+7z=812$, find $x+y+z$.

harina [27]

Answer:

10

Step-by-step explanation:

When we simplify we get $z(6xy+21x+2y+7)+30xy+105x+10y=812.$

Then we continue to factor to get: $(z+5)(6xy+21x+2y+7)&=847.$

We then see that we can factor $(6xy+21x+2y+7)$ into $(z+5)(3x+1)(2y+7)&=847.$

we then do the prime factorization of 847, which i think is, $7*11*11$ . we have to find the numbers that multiply to 847 and then plug them into z+5, 3x=1,2y+7.

It has to be a positive, non-negative integer, right?

We also see that 3x+1=11 so we see that x=10/3 (which wont work).

So 3x+1=7, so x=2.

So 11 has to be in another term. It has to be in 2y+7=11 so y=2

for the last term we get z+5=11 so z=6

2+2+6=10

Hope this helps and if you want please consider giving me brainliest. :)

8 0

3 years ago