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fiasKO [112]
3 years ago
14

Solve for z. 1+2z<5.

Mathematics
1 answer:
Ksju [112]3 years ago
5 0

Answer:

z < 2

Step-by-step explanation:

1 + 2z < 5

<u>-1          -1</u>

2z  < 4

z < 4 ÷ 2

z < 2

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Find an equation for the perpendicular bisector of the line segment whose endpoints are (5,-9)and (-9,-5)
Papessa [141]

Answer:

y = ¹⁴/₄.x

Step-by-step explanation:

First of, if the bisector is perpendicular to the line segment, then we can find the gradient of the bisector (m_{b}) using the rule/principle:

Let:

m = gradient of the line segment

Then:

m_{b} = -\frac{1}{m}

We can find m since we have two points that fall on the line segment, (5, -9) and (-9, -5):

m = Δy/Δx

m = \frac{-9 - (-5)}{5 - (-9)} \\\\ m = -\frac{4}{14}

We can now find m_{b}:

m_{b} = -\frac{1}{(-\frac{4}{14}) } \\\\ m_{b} = 1.\frac{14}{4} \\\\ m_{b} = \frac{14}{4}

The equation of a line can be found using:

y - y₁ = m(x - x₁)

We have the gradient of the perpendicular bisector, the only other thing we need to identify the equation of the bisector is coordinates of a point that fall on the line;

We know the line will pass through the point exactly midway between (5, -9) and (-9, -5) since it is a bisector;

This can be found by:

x_{1} = -9 + \frac{5 - (-9)}{2} \\ x_{1} = -9 + 7 \\ x_{1} = -2 \\\\ y_{1} = -5 + \frac{-9 - (-5)}{2} \\ y_{1} = -5 +(-2) \\ y_{1} = -7 \\\\ (-2, -7)

We have a point on the line and the gradient so we can now find the equation:

y - (-7) = \frac{14}{4}(x - (-2)) \\\\ y + 7 = \frac{14}{4}(x + 2) \\\\ 4y + 28 = 14(x + 2) \\\\ 4y + 28 = 14x + 28 \\\\ 4y = 14x \\\\ y = \frac{14x}{4}

8 0
3 years ago
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. How many oranges are in the pile?
gayaneshka [121]
Short Answer D
P(1) = 1(1+1)(2*1 + 1)/6
P(1) = 1(2)(2 +1) / 6
P(1) = 1(2)(3)/6
P(1) = 1

P(2) = 2(2+1)(2*2 + 1) / 6
P(2) = 2(3)(5) / 6
P(2) = 5 So this formula is adding as it goes along. To Find the Total all we need do is use the formula to calculate P(1) to P(7)

P(7) = 7*(7 + 1)(2*7 + 1)/6
P(7) = 7 * 8 * 15 / 6
P(7) = 7 * 4 * 5 
P(7) = 140 <<<< Answer
4 0
4 years ago
How are exponents helpful?
ICE Princess25 [194]
Exponents help to get to the answer if you are doing an equation, They are meant to tell you and help you with the proper order of pemdas!
3 0
4 years ago
Find the area of the following<br> parallelogram:<br> 1.5 cm<br> 2.5 cm<br> 2.25 cm<br> A= [?] cm
Serggg [28]

Answer:

given,

base (b) = 2.25cm

height (h) = 1.5 cm

now,

area (a) = b×h

or, a=2.25cm×1.5cm

therefore the area of parallelogram is 3.375cm^2.

<em>hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em><em>.</em>

7 0
3 years ago
Find the missing side
miv72 [106K]

Answer:

\sqrt{29}

Step-by-step explanation:

You would use the Pythagorean Theorem: a^{2} + b^{2} = c^{2}

The a and b is the legs and the c is the hypotenuse

So when you fill it in you get 2^{2} + 5^{2} = c^{2}

continue to solve the equation 4+25= c^{2}

29 = c^{2}

then you would square root it

c = \sqrt{29}

6 0
3 years ago
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