Foundation Geometry

A. 57*
B. 90*
C.33*
D.67*

Answer:

m = -1/2

Step-by-step explanation:

Recall that slope = (change in y) / (change in x).

Going from  (−8,−1) to (−6,−2), x increases by 2 (because -6 - (-8) = 2), and

y decreases by 1.  Thus, the slope here is

m = (change in y) / (change in x) = (-1) / 2 = -1 / 2

m = -1/2

Answer:

Angle Z is 70 degrees

Step-by-step explanation:

The 3 angles of a triangle add up to 180 degrees. Angle x is 45, angle y is 65.

180-45-65 = 180-110 = 70

Answer: The answer is the option A.

x=(5±)/4

Step-by-step explanation: The quadratic formula has the following form for a quadratic equation ax²+bx+c:

x=(-b±))/(2a)

We apply the quadratic formula and we obtain:

x=(-(-5)±))/(2(2))

x=(-(-5)±))/(4)

x=(-(-5)±))/(4)

Answer:

on day 6

Step-by-step explanation:

you would multiply

Answer:

4^10

subtract 15-5 and leave the 14 be

Answer:

14 to the tenth power

Step-by-step explanation:

fifteen - fifth = ten. When you are working on exponential problems like this, remember to add or subtract the powers.

Answer:

graph points (0,2) and (0.857,0)

Step-by-step explanation:

can i please have the brainliest

Answer:

No.

Step-by-step explanation:

First solve for y:-

x - y^4 = 1

y^4 = x - 1

y = +/- (x - 1)^(1/4)

This is a one-to-many relation . For a given value of y there  2 values of x.

So this is NOT a function.

Answer:

The area is 49/12 or 4 1/12

Step-by-step explanation:

The area of a triangle is:

a = 1/2 × base × height

a = 1/2 × 3 1/2 × 2 1/3 (4 2/3 is not the height!)

a = 1/2 x 7/2 x 7/3 (I converted all the fractions into improper fractions)

a = 49/12 (1 × 7 × 7 = 49, 2 × 2 × 3 = 12)

You can convert it back to a mixed number:

49/12 = 4 1/12

Hope this helps!

Answer:

here you go.

Step-by-step explanation:

The diagonal is the hypotenuse of a rectangular triangle.

So:

d2=l2+w2 

132=169=(x+7)2+x2=x2+14x+49+x2→

2x2+14x−120=0→x2+7x−60=0

A simple quadratic equation resolving into:

(x+12)(x−5)=0→x=−12orx=5

Only the positive solution is useable so:

w=5andl=12

Step-by-step explanation:

(21 - 3) ÷ 32

BIDMAS

Brackets: 21 - 3 = 18

Division: 18 ÷ 32 = (0.5625)

Answer:

128º

Step-by-step explanation:

You just add the two angles together

<GFE=<KFE+<GFK

<GFE=100+28

<GFE=128

Answer:

82,000+7500+1,386=168,136

Step-by-step explanation:

You have to do Addition

The earning of the salesperson is an illustration of a linear function.

The possible functions in the two scenarios are: [tex]\mathbf{I(s) = 0.1s + 2500}[/tex] and [tex]\mathbf{I(s) = 0.05s + 2000}\\[/tex]

The function is given as:

[tex]\mathbf{I(s) = 0.1s + 2000}[/tex]

When the base salary is increased, a possible function is:

[tex]\mathbf{I(s) = 0.1s + 2500}[/tex]

This is so, because 2500 is greater than 2000

When the commission rate is decreased, a possible function is:

[tex]\mathbf{I(s) = 0.05s + 2000}\\[/tex]

This is so, because 0.05 is less than 0.1

So, the possible functions in the two scenarios are:

[tex]\mathbf{I(s) = 0.1s + 2500}[/tex] and [tex]\mathbf{I(s) = 0.05s + 2000}\\[/tex]

See attachment for the graphs of both functions

Read more about linear equations at:

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Answer:true,true,false, true,false false

Step-by-step explanation:

Answer:

As shown in the attachment,

Step-by-step explanation:

Answer:

15 and 45

Step-by-step explanation:

15*3=45

15+45=60

hope this helps!

The inequality that represents all possible values for x is  x ≥ -27.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The given statement can be written in terms of inequality as,

2/3x - 6 ≥ -24

=> 2/3x  ≥ -24 + 6

=> 2/3x  ≥ -18

=> x ≥ -27

Hence, the inequality expression for the given problem can be written as x ≥ -27.

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Answer:

I'm pretty sure that's an angle.

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Given arithmetic sequence

3,5,7,9,.........,21

The first term a=3 & a common difference d=5−3=7−5=⋯=2

If there are n number of terms in the above A.P. then last term l=21 will be the nth term given as

l=a+(n−1)d

21=3+(n−1)2

n=10

hence the sum of given arithmetic progression (A.P.) up to 10 terms is given general formula

Sn=n2(a+l)

S10=102(3+21)

=120

Answer:

y-4=3.1(x-1)

or y-1.6=3.1(x-1.4)

Step-by-step explanation:

Answer:

y = 3.1x - 2.74

Step-by-step explanation:

y-intercept: 1.6 - (3.1)(1.4) = 1.6 - 4.34

= - 2.74

Answer:

Yes, because the 39 books and 21 cds price is proportional to the 52 books and 28 cds' price

Step-by-step explanation:

:>

Answer: D

Step-by-step explanation:

Answer:$22.50

Step-by-step explanation:

The three friends already paid the entrance fee. The question asks how much MORE will they pay for 5 MORE rides (8-3 rides). Since tickets are $1.50 each, and we have 3 people:

($1.50/ticket)*(5 tickets/person)*(3 persons) = $22.50 more.

[Note how the units cancel, leaving just $]

Answer:

Step-by-step explanation:

y > 3x + 10

y < -3x - 1

You'd graph the given systems of linear inequalities the same way as you graph the linear equations.  

To graph y > 3x + 10, plot the y-intercept, (0, 10), then use the slope, m = 3 (rise 3, run 1), to plot other points on the graph.  Use a dashed line (because of the ">" symbol).  

Follow the same steps for the other linear inequality. Plot the y-intercept, (0, -1), then use the slope, m = -3 (down 3, run 1) to plot other points. Use a dashed line (because of the "<" symbol).  

Pick a test point on either side of the boundary line and plug it into the original problem.  This will help determine which side of the boundary line is the solution.  Plug in a test point that is not on the boundary line.

Use the point of origin, (0, 0) as the test point. Plug in these values into the given systems of linear inequalities to see whether it will provide a true statement.  

y > 3x + 10

0 > 3(0) + 10

0 > 0 + 10

0 > 10 (False statement).  

y < -3x - 1

0 < -3(0) - 1

0 < 0 - 1

0 < -1 (false statement).  

Since the point of origin provided a false statement to the given systems of linear inequalities, you must shade the half-plane region where it doesn't contain the test point.  

You'll do the same process as what I've done for the test point. Plug in the values of (8, 10) into the given systems of linear inequalities. If it provides a false statement, then it means that it is not a solution to the system.  

y > 3x + 10

10 > 3(8) + 10

10 > 24 + 10

10 > 34 (False statement).  

y < -3x - 1  

10 < -3(8) - 1

10 < -24 - 1

10 < -25 (false statement).  

Therefore, (8, 10) is not a solution to the system.    

Answer:$4,650.00

Step-by-step explanation:35,000x10%=3,500

3,500+1,150=4,650

Answer:

7344 (yo i haven't done this since like 5th grade so i dont know if its right)

Step-by-step explanation:

800 increase by %2 is 816

816 x 9 = 7344

Answer:

[tex]3x - 9 = 2x + 21 \\ 3x - 2x - 9 = 2x - 2x + 21 \\ x - 9 = 21 \\ x - 9 + 9 = 21 + 9 \\ x = 30[/tex]

m<DGI = 80°

[tex]3x - 9 = \\ 3(30) - 9 = \\ 90 - 9 = 81[/tex]

The measure of angle ∠DGI can be obtained by finding the solution of the equation as 81°.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The ray GI bisects ∠DGH.

It implies that the new angles are equal in measurement.

⇒ m∠DGI = m∠IGH

⇒ 3x - 9 = 2x + 21

⇒ x = 30

Then, in order to calculate m∠DGI, plug x = 30 in  3x - 9 as,

3 × 30 - 9 = 81

Hence, the measure of angle ∠DGI is given as 81°.

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Using quadratic function concepts, it is found that:

1) The equation is [tex]y = -0.08x^2 + 4x[/tex]

2) The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.

A quadratic equation has the following format:

[tex]y = ax^2 + bx + c[/tex]

In this problem:

Item 1:

The vertex is: [tex]V(x_v,y_v)[/tex], in which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, it is (25,50). Thus:

[tex]-\frac{b}{2a} = 25[/tex]

[tex]-b = 50a[/tex]

[tex]b = -50a[/tex]

[tex]-\frac{b^2 - 4ac}{4a} = 50[/tex]

[tex]-b^2 = 200a[/tex]

[tex]-(50a)^2 = 200a[/tex]

[tex]-2500a^2 - 200a = 0[/tex]

[tex]200a(-12.5a - 1) = 0[/tex]

Then, as [tex]a \neq 0[/tex]

[tex]a = -\frac{1}{12.5} = -0.08[/tex]

[tex]b = -50a = -50(-0.08) = 4[/tex]

Thus, the equation, in standard form, is:

[tex]y = -0.08x^2 + 4x[/tex]

Item 2:

The distances are the values of x for which:

[tex]y = 10[/tex]

Then

[tex]-0.08x^2 + 4x = 10[/tex]

[tex]-0.08x^2 + 4x - 10 = 0[/tex]

Which is a quadratic equation with [tex]a = -0.08, b = 4, c = -10[/tex]. Then:

[tex]\Delta = 4^2 - 4(-0.08)(-10) = 12.8[/tex]

[tex]x_{1} = \frac{-4 + \sqrt{12.8}}{2(-0.08)} = 2.64[/tex]

[tex]x_{2} = \frac{-4 - \sqrt{12.8}}{2(-0.08)} = 47.36[/tex]  

The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.

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Answer:

10/21

Step-by-step explanation:

Number of minutes required for printing 21 pages: 10

So, number of minutes required for printing 1 page

= 10/21

(= 0.47 = 0.5 [approximately])

Answer:

-9/6 or -3/2

Step-by-step explanation:

To find the x intercept, substitute y = 0 into the equation:

6x + 3(0) = -9

Now simplify,

6x + 0 = -9

6x = -9

x = -9/6 → -3/2

Tip: If you were finding the y-intercept, you would substitute x = 0 into the equation instead

Answer:

Step 1: Calculate

We calculate the square root of 23 to be:

√23 = 4.79583152331272

Step 2: Reduce

Reduce the tail of the answer above to two numbers after the decimal point:

4.79

Step 3: Round

Round 4.79 so you only have one digit after the decimal point to get the answer:

4.8

To check that the answer is correct, use your calculator to confirm that 4.82 is about 23.

The negative square root of 23 to the nearest tenth will lie between 4 and 5 on the number line and more closer to 5.

Number which are formed by multiplying a number with itself once are called perfect square numbers.

Now the given number is,

negative square root of 23

Thus we have, [tex]-\sqrt{23}[/tex]

So the value of [tex]-\sqrt{23}[/tex]  is -4.79

To round to the nearest tenth, so the digit at the tenth place is 7 and digit at right of 7 is 9 which is greater than 5 so roundup the digit.

Thus we get,
[tex]-\sqrt{23}[/tex] = 4.8

Thus, this point will lie between 4 and 5 and more closer to 5.

Thus, the negative square root of 23 to the nearest tenth will lie between 4 and 5 on the number line and more closer to 5.

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