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
Ulleksa [173]
3 years ago
9

Direction: Determine whether the given point is a solution to the given system of linear inequalities.

Mathematics
1 answer:
Ann [662]3 years ago
8 0

Answer:

The given point is a solution to the given system of inequalities.

Step-by-step explanation:

Again, we can substitute the coordinates of the given point into the system of inequalities. We know that the x-coordinate and y-coordinate of (3,2) are x=3 and y=2, respectively.

Plugging these values into the first inequality, y\leq x+3, gives us 2\leq 3+3, which simplifies to 2\leq 6. This is a true statement, so the given point satisfies the first inequality. We still need to check if it satisfies the second inequality though, because if it doesn't, it won't be a solution to the system.

Plugging the coordinates into the second inequality, y\geq -x+3, gives us 2\geq -3+3, which simplifies to 2\geq 0. This is also a true statement, so the given point satisfies the second inequality as well. Therefore, \bold(\bold3\bold,\bold2\bold) is a solution to the given system of inequalities since it satisfies all of the inequalities in the system. Hope this helps!

You might be interested in
Please help me asap i will give brainiest and all my points
Alinara [238K]

Answer:

a. Not Divisible

b. Divisible

c. Divisible

d. Divisible

e. Divisible

Step-by-step explanation:

To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.

Let's begin with a:

16^{5}+215 by 33

1,048,576 + 215

1,048,791

We now then divide the total amount with 33.

\dfrac{1,048,576}{33}

= 31,781.5454

We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.

Now let's continue on with the others.

51^{7}-51^{6} by 25

897,410,677,851 - 17,596,287,801

879,814,390,050

We now then divide the total amount with 25.

\dfrac{879,814,390,050}{25}

= 35,192,575,602

The total value did NOT return a decimal point, therefore making the equation true. 51^{7}-51^{6} IS divisible by 25.

Next on we have:

5^{5}-5^{4} +5^{3} by 7

3,125 - 625 + 125

As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.

2,500 + 125

2,625

We now then divide the total amount with 7.

\dfrac{2,625}{7}

= 375

The total value did NOT return a decimal point, therefore making the equation true. 5^{5}-5^{4} +5^{3} IS divisible by 7.

7^6+7^5-7^4 by 11

117,649+16,807-2,401

134,456-2,401

132,055

We now then divide the total amount with 11.

\dfrac{132,055}{11}

= 12,005

The total value did NOT return a decimal point, therefore making the equation true. 7^6+7^5-7^4 IS divisible by 11.

Last but not the least:

5^{23}-5^{21} by 24

11,920,928,955,078,125-476,837,158,203,125

11,444,091,796,875,000

We now then divide the total amount with 24.

\dfrac{11,444,091,796,875,000}{24}

= 476,837,158,203,125

The total value did NOT return a decimal point, therefore making the equation true. 5^{23}-5^{21} IS divisible by 24.

5 0
3 years ago
Which of the following scales of measurement lacks numeric properties?
Rus_ich [418]

Answer: A

Step-by-step explanation:

The nominal scale by definition only deals with non-numeric or non-quantitative variables or where numbers have no numerical value. The nominal scale uses tags or labels instead of number to classify or identify an object being measured.

5 0
3 years ago
Find the quadratic function y=​f(x) whose graph has a vertex ​(−3​,4​) and passes through the point ​(−7​,0). Write the function
olganol [36]

Answer:

Step-by-step explanation:

This is a parabola since a quadratic is a parabola.  The standard form for a parabola is y = ax² + bx + c

but before we do that, we will use the vertex form, since it will make our work easier at the beginning.  

First and foremost, when we plot the vertex and the given point, the vertex is higher up than is the point; that means that this parabola opens upside down, and its vertex form will be

y=-|a|(x - h)² + k

The absolute value is out in front of the a, so we know that the value of a is positive, but the quadratic itself is negative (upside down) and we will find that math takes care of that negative that needs to be out front.  So we need to solve for a by filling in the x, y, h, and k values from the point and the vertex:  x = -7, y = 0, h = -3, k = 4

0 = a(-7 - (-3))² + 4 and

0 = a(-7 + 3)² + 4 and

0 = a(-4)² + 4 and

0 = a(16) + 4 and

0 = 16a + 4 and

-4 = 16a so

a=-\frac{1}{4}

Now that we know a, we can plug it back into the vertex form and then put it into standard form from there.

y=-\frac{1}{4}(x+3)^2+4

Now we will FOIL out what's inside the parenthesis to get

y=-\frac{1}{4}(x^2+6x+9)+4

Simplify by distributing the -1/4 into the parenthesis:

y=-\frac{1}{4}x^2-\frac{3}{2}x-\frac{9}{4}+4

Combine like terms to get

y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{7}{4}

And there you go!

5 0
3 years ago
Together, Bobs shoes weigh about 1 kilograms. Each shoe weighsabout how many grams.
kolbaska11 [484]
Divide 1 kilogram by how much shoes are there.
8 0
3 years ago
Read 2 more answers
10-2+3x19-8= first to answer will get brainlyest
KIM [24]
57 because of pemdas....
3 0
2 years ago
Read 2 more answers
Other questions:
  • If you bought a stock last year for a price of $67, and it has risen 12% since then, how much is the stock worth now, to the nea
    8·1 answer
  • an arc subtends a central angle measuring 2pi/3 radians. what fraction of the circumference is this arc?
    7·1 answer
  • WILL GIVE BRAINLIEST!<br> What’s the perimeter and area of this figure?
    10·1 answer
  • Can somone please help me and explain very much appreciated and this is 7th grade math btw
    15·1 answer
  • How do I workout/find the unknown angles please
    5·1 answer
  • Which one shows a proportional relationship between x and y<br> Y=9x or y=10x
    13·1 answer
  • Is the value 5 a solution to the inequality r + 4 &lt; 7 ?
    6·2 answers
  • What is the Prime Factorization of 108?
    14·2 answers
  • Help please I will mark you as brainly
    6·2 answers
  • Which expression is equivalent to
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!