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3 years ago

Identify the vertex of the parabola given by f(x) = (x + 2)^2 – 4

Mathematics

1 answer:

kicyunya [14]3 years ago

8 0

Answer:

The vertex is ( -2, -4)

Step-by-step explanation:

The vertex form is

y = a( x-h) ^2 +k

where ( h,k) is the vertex

f(x) = (x + 2)^2 – 4

Rewriting

f(x) = (x - -2)^2 – 4

The vertex is ( -2, -4)

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Note that WXYZ has vertices W(-1, 2), X(-5, 7), y(-1, -2), and Z (3, -7).

svp [43]

a. Slope of WZ = -2.25; Slope of WX = 5

b. WZ = √97; WX = √41

c. WXYZ is not a <em>rectangle, rhombus, nor a square</em>. We can conclude that: <em>D. WXYZ is none of these</em>.

<h3>Slope of a Segment</h3>

Slope = change in y/change in x

Given:

W(-1, 2), X(-5, 7), Y(-1, -2), and Z (3, -7)

a. Slope of WZ and slope of WX:

Slope of WZ = (-7 - 2)/(3 -(-1)) = -2.25

Slope of WX = (7 - 2)/(-1 -(-1)) = 5

b. Use distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ , to find WZ and WX:

$WZ = \sqrt{(3 - (-1))^2 + (-7 - 2)^2}\\\\\mathbf{WZ = \sqrt{97} }$

$WX = \sqrt{(-5 -(-1))^2 + (7 - 2)^2}\\\\\mathbf{WX = \sqrt{41} }$

c. The quadrilateral WXYZ have adjacent sides that are not perpendicular to each other and have different slopes and different lengths, so therefore, WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: <em>D. WXYZ is none of these</em>.

Learn more about slopes on:

brainly.com/question/3493733

5 0

3 years ago

Jalen is buying a new car. He has the options below.

EleoNora [17]

The total number of choices Jalen has is six

7 0

3 years ago

Read 3 more answers

3. If each person paid an equal amount, who would save the most money? Explain your reasoning using at least two complete senten

Rzqust [24]

There ar 4persons so each will pay

$\\ \sf\longmapsto \dfrac{83.90}{4}=20.975$

Only two persons have spent more money than everyone average i.e mia and Jasmin.

Now

Mia has-28.47
Jasmin has=20.99

Mia left more money so she saved most money.

7 0

3 years ago

Si -x+y+z=75, entonces -(x+3)+(y-5)+(z-6)=

jenyasd209 [6]

Answer:

Step-by-step explanation:

● -(x + 3) + (y - 5) + (z - 6)

● -x - 3 + y - 5 + z - 6

● (-x + y + z) + (3 -5 -6)

● 75 + 3 - 11

● 78 - 11

● 67

8 0

3 years ago

Investigate the difference between compounding annually and simple interest

Gennadij [26K]

Step-by-step explanation:

Simple interest formula

$A = P (1 + rt)$

Compound interest formula

$A = P(1 + \frac{r}{n})^{nt}$

$A = 5000 (1 + 0.025*1)\\A=5000(1.025)\\A=5125$

Simple interest is $125

. $A = 5000 (1 + \frac{0.025}{1})^{1*1} \\A=5000(1.025)\\A= 5125$

Compound interest is $125

c. the result for both a and b are the same

$A = 5000 (1 + 0.025*3) \\A=5000(1.075) \\A=5375$

the simple interest is $375

. $A = 5000 (1 + \frac{0.025}{1})^{1*3}] \\A=5000(1.025)^3 \\A=5000(1.077)\\A= 5385$

the compound interest is $385

f. the result compared, compound interest is $10 more than simple interest

$A = 5000 (1 + 0.02*6) \\A=5000(1.12) \\A=5600$

the simple interest is $600

$A = 5000 (1 + \frac{0.02}{1})^{1*6}] \\A=5000(1.12)^6 \\A=5000(1.9738) \\A= 9869$

the compound interest is $4869

i. the result from g and h, h is over 8 times bigger than g.

j. interest compound annually is not the same as simple interest, only for the case of a and b seeing that it is for 1 year. but for 2years and above there is difference as seen in c to h

6 0

3 years ago