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KatRina [158]
3 years ago
10

Solve (x + 1 < 5) ∩ (x - 4 > -3).

Mathematics
1 answer:
NikAS [45]3 years ago
8 0

Answer:

{all real numbers}

Step-by-step explanation:

Solve (x + 1 < 5) ∩ (x - 4 > -3).

For the expression

x + 1 < 5

Subtract 1 from both sides

x+1-1 < 5-1

x < 4

For the inequality

x - 4 > -3

Add 4 to both sodes

x-4+4 > -3 + 4

x > -1

Hence the intersection of both is on all real numbers since the value of x is greater than -1.

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Explain why the graph of quadratic function could not contain both a minimum vertex and a maximum vertex at the same time.
KonstantinChe [14]
A quadratic function is a function of the form f(x)=ax^2+bx+c. The vertex, (h,k) of a quadratic function is determined by the formula: h= \frac{-b}{2a} and k=f(h); where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. The value of a determines if the <span>parabola opens upward or downward; if</span>a is positive, the parabola<span> opens upward and the vertex is the minimum value, but if </span>a is negative <span>the graph opens downward and the vertex is the maximum value. Since the quadratic function only has one vertex, it </span><span>could not contain both a minimum vertex and a maximum vertex at the same time.</span>
3 0
4 years ago
Aquelyn’s earning m are a function of the number of lawns n she mows at a rate of $12 per lawn
nekit [7.7K]

Answer:

m = 12n

Step-by-step explanation:

M is the amount that she would earn at the end of the day. She charges 12 dollars per lawn and then you multiply that by n which is going to be how many lawns she mowed.

4 0
3 years ago
What is the area of a regular heptagon with side length of 6 meters and a distance from the to the vertex of 6 meters? round you
Ahat [919]
Apothem = side length / 2*tan(180 / number of sides)
apothem = side length / 2*tan (180 / 7)
apothem = 6 / (2*tan( <span> <span> <span> 25.7142857143</span></span></span>))
apothem = 6 / 2*0.48157
<span><span><span>apothem = 6.2296239384 </span> </span> </span>

Polygon area = (# of sides * side length * apothem) / 2
Polygon area = ( 7 * 6 * <span>6.2296239384) / 2
</span><span><span><span>Polygon area = 130.8221027064 </span> </span> </span> 



8 0
3 years ago
What is 1/12 of 162.56
butalik [34]
The answer would be 13.546

you would do 162.56 divided by 12.
4 0
3 years ago
Deonte invested 200000at his bank for 10 years if he earned 130000 what was the interest rate the bank gave him
Volgvan

<u>Answer:</u>

The interest rate the bank gave Deonte is 6.5%.

<u>Solution:</u>

Given, Deonte invested 200000 at his bank for 10 years  

He earned 130000  

We have to find what was the interest rate the bank gave him.

Now we know that, simple interest =\frac{\text {amount} \times \text {rate} \times \text {time}}{100}

So, by substituting our values in above formula,

130000=\frac{200000 \times \text { rate } \times 10}{100}

Interest rate \times 20000 = 130000

Interest rate \times 2 = 13

\text { Interest rate }=\frac{13}{2}=6.5 \%

Hence, the interest rate given by bank is 6.5% to Deonte.

8 0
3 years ago
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