7.064 and expanded form

Sidana [21]

For each of the problems for example #11 tells you to find the measure of angle ABC ABH=46 HBC=120
Therefore you just add the 2 together to get 166
So for #12 its a little diffrent the line is straight so it equals 180 degrees they give you one angle so 180-95= 85
Makes sense?

6 0

3 years ago

The expression LaTeX: -5t^2+40t

dlinn [17]

Answer:

8 seconds

Step-by-step explanation:

Given

h = - 5t² + 40t

When the object hits the ground then h = 0

Substitute h = 0 into the function and solve for t

- 5t² + 40t = 0 ← factor out - 5t from each term

- 5t(t - 8) = 0

Equate each factor to zero and solve for t

- 5t = 0 ⇒ t = 0

t - 8 = 0 ⇒ t = 8

t= 0 denotes the time of launch

t = 8 denotes the time it hits the ground

7 0

3 years ago

Two princesses, Nat and Kat, are gifted with a savings account from their royal parents, Matt and Pat, when they turn 5 years ol

Arte-miy333 [17]

Answers and Step-by-step explanations:

(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:

m = (21200 - 6200) / (7 - 2) = 3000

Now, we have y = 3000x + b. Plug in 6200 for y and 2 for x to solve for b:

y = 3000x + b

6200 = 3000 * 2 + b

b = 200

Nat's equation is y = 3000t + 200.

(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:

y = a(x - h)² + k, where (h, k) is the vertex

Plug in our vertex:

y = a(x - 20)² + 44100

We also have the point (9, 32000), so put that in to find a:

32000 = a(9 - 20)² + 44100

-12100 = a * 121

a = -100

So Kat's equation is y = -100(t - 20)² + 44100.

(c) In order to find the age when they have the same amount, we set the two equations equal:

3000t + 200 = -100(t - 20)² + 44100

-100(t² - 40t + 400) + 44100 = 3000t + 200

-100t² + 4000t - 40000 + 44100 - 3000t - 200 = 0

-100t² + 1000t + 3900 = 0

t² - 10t - 39 = 0

(t - 13)(t + 3) = 0

t = 13 or t = -3 -- obviously, years can't be negative, so t = 13.

Note, however, that t is the number of years <em>after</em> Kat and Nat are 5, so we need to add 13 to 5:

13 + 5 = 18

The age is 18.

4 0

3 years ago

Read 2 more answers

For the linear equation 3x + 7y = 42: a. Determine the slope: b. Determine y- intercept if it exists: c. Express equation in slo

algol13

Answer: The required answers are

(a) the slope of the given line is $-\dfrac{3}{7}.$

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is $y=-\dfrac{3}{7}x+6.$

Step-by-step explanation: We are given the following linear equation in two variables :

$3x+7y=42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to :

(a) determine the slope,

(b) determine the y-intercept, if exists

and

(c) express equation in slope-intercept form.

We know that

The SLOPE_INTERCEPT form of the equation of a straight line is given by

$y=mx+c,$ where m is the slope and c is the y-intercept of the line.

From equation (i), we have

$3x+7y=42\\\\\Rightarrow 7y=-3x+42\\\\\Rightarrow y=\dfrac{-3x+42}{7}\\\\\\\Rightarrow y=-\dfrac{3}{7}x+6.$

Comparing with the slope-intercept form, we get

$\textup{slope, m}=-\dfrac{3}{7},\\\\\\\textup{y-intercept, c}=6.$

Thus,

(a) the slope of the given line is $-\dfrac{3}{7}.$

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is $y=-\dfrac{3}{7}x+6.$

3 0

3 years ago

I need help, help me plz !!!!! Match the verbal expression (term) with its algebraic expression (definition). Match Term Definit

Talja [164]

Answer:

Four less than an unknown value E) $y-4$

Quotient of a variable and four B) $\frac{z}{4}$

Some number to the power of four A) $a^4$

Four times an unknown value D) $4x$

Four more than some number C) $b+4$

Step-by-step explanation:

Let's analyze each statement separately:

- Four less than an unknown value --> this means that we have to subtract 4 to an unknown value. Calling $y$ the unknown value, it means we have to write

$y-4$

- Quotient of a variable and four --> this means we have to divide a variable by 4. Calling $z$ the unknown variabl, it means we have to write

$\frac{z}{4}$

- Some number to the power of four --> this means that we have to write the power of a number, in the form $a^m$ , where m in this case is equal to 4. Calling $a$ the unknown number, it means we have to write

$a^4$

- Four times an unknown value --> this means that we have to multiply an unknown value by 4. Calling $x$ our unknown values, we have to write

$4x$

- Four more than some number --> this means we have to add 4 to an unknown number. Calling $b$ the unknown number, it means we have to write

$b+4$

7 0

3 years ago

Read 2 more answers

7.064 and expanded form ​

7.064 and expanded form