Willow has a recipe that asks her to use 3/4 cup of sugar. She is going to make 1/2 of the recipe, so she only needs 1/2 of that 3/4 cup. How many cups of sugar will she use?

Answer:

f(2)=0

Step-by-step explanation:

You plug in 2 for any X's in the equation

f(2)=2^2-4

Answer:

answers?

Step-by-step explanation:

60% of 500 is 300

So if Zack wanted to sell the car 60% of the markets price, it would be 300.

125% of 500 is 625

If Zack wanted to sell the car for 25 more than the price at market, it would be 125%, and 125% of 500 is 625.

9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

In order for TV to be parallel to QS, it must divide the sides of the triangle proportionally.

  RT/TQ = RV/VS

  (x+4)/(x-3) = (x+10)/(x)

  1 +7/(x-3) = 1 +10/x . . . . expand each fraction

  7/(x -3) = 10/x . . . . . . . . subtract 1

  7x = 10(x -3) . . . . . . . . . cross multiply

  30 = 3x . . . . . . . . . . . . add 30-7x, simplify

  10 = x . . . . . . . . . . . . . . divide by 3

The value of x that makes the segments parallel is 10.

_____

Alternate solution

You can cross multiply the first fraction we wrote to get ...

  x(x +4) = (x -3)(x +10)

  x^2 +4x = x^2 +7x -30 . . . eliminate parentheses

  30 = 3x . . . . . . subtract x^2+4x-30 from both sides

Answer: C. 10

Step-by-step explanation:

i got it right on the test

Answer:

Step-by-step explanation:

Distance from home plate to second base = 90√2 feet

Distance from third base to first base = 90√2 feet

60 ft 6 in = 60.5 ft

90√2 /2 = 45√2 ≅ 63.6 ft ≠ 60.5 ft

The pitcher's mound is not at the midpoint.

Answer:

18 foot ladder will reach at 14.4 feet up the wall.

Step-by-step explanation:

Triangles formed by the ladder against wall and the ground are similar,

ΔABC ~ ΔDEC

Therefore, their corresponding sides will be proportional.

[tex]\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}[/tex]

[tex]\frac{AB}{DE}= \frac{BC}{EC}[/tex]

[tex]\frac{18}{10}=\frac{BC}{8}[/tex]

BC = [tex]\frac{18\times 8}{10}[/tex]

     = 14.4

Therefore, 18 foot ladder will reach at 14.4 feet up the wall.

Answer:

the statement would be false.

Step-by-step explanation:

Jenny sold 17 less than 3 times lauras 4 quilts. So that would make Laura have 12 and 12<17.

Answer:

20 floors

Step-by-step explanation:

15 sec to go up 5 floors is climbing one floor every 3 seconds

3 sec x 20 = 60 seconds

1 fl x 20 = 20 floors

Answer:

Answer: 20pi is the circumference

Step-by-step explanation:

The circumference of the circle is 20π ft when the area of the circle is 100π ft².

A circle is a locus of the points drawn at an equidistant from a fixed point. The fixed point is called Centre of the circle and the distance from the fixed point to the circle is called radius.

Given, area of a circle is 100π.

Therefore,  πr² =100π, where r is the radius of the circle.

So, r²=100

Thus, r= 10 ft.

now, circumference = 2πr

                                  =2π×10

                                  =20π ft.

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Answer:

Step-by-step explanation:

Average of x-coordinates = (8+3)/2 = 5.5

Average of y-coordinates = (5+7)/2 = 6

Midpoint at (5.5,6)

9514 1404 393

Answer:

  2^17×3^7

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

__

  [tex](2^9\times3^5)\times(2^4\times3)^2=2^9\times3^5\times2^{4\cdot2}\times3^2\\\\=2^{9+8}\times3^{5+2}=\boxed{2^{17}\times3^7}[/tex]

Answer:  (1) [tex]y= \sqrt{x+2}-2[/tex]   (2) y = (x - 3)³

                    D: x ≥ -2  [-2, ∞)      D: -∞ < x < ∞ (-∞, ∞)

                    R: y ≥ -2  [-2, ∞)      R: -∞ < y < ∞ (-∞, ∞)

                    Inc: x > 2 (2, ∞)      Inc: (-∞, 3) ∪ (3, ∞)

                    Dec: never             Dec: never

Step-by-step explanation:

NOTES:

Domain is the x-values.

Range is the y-values.

From left to right: increasing when going up and decreasing when going down. The anchor and turning point are not considered to be increasing or decreasing.

Let f(x) = ax ³ + bx ² + cx + d.

The graph of f(x) passes through (4, -22) and (3, -26), which means f (4) = -22 and f (3) = -26, so that

64a + 16b + 4c + d = -22

27a + 9b + 3c + d = -26

When the question says it has tangents at some point, I take that to mean the slope of the tangent line at that point is the given number. So f ' (4) = 11 and f ' (3) = -2. We have

f '(x) = 3ax ²+ 2bx + c

so that

48a + 8b + c = 11

27a + 6b + c = -2

Solve the system:

• Eliminate d :

(64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -22 - (-26)

→   37a + 7b + c = 4

• Eliminate c :

(48a + 8b + c) - (27a + 6b + c) = 11 - (-2)

→   21a + 2b = 13

(48a + 8b + c) - (37a + 7b + c) = 11 - 4

→   11a + b = 7

• Eliminate b, then solve for a and the other variables:

(21a + 2b) - 2 (11a + b) = 13 - 2 (7)

-a = -1

a = 1   →   b = -4   →   c = -5   →   d = -2

Then

f(x) = x ³ - 4x ² - 5x - 2

Answer:

Undefined

Step-by-step explanation:

Answer:

2x + x +90= 180 We will add 2x + x=3x We get 3x + 90 =180 Now we subtract 3x = 180–90 ... x=30, for confirmation put value of x =30in equation and verify. LHS=RHS. Thats it. 68 views.

Given:

A circle with radius 7 units and chord CD = 7 units.

To find:

The measure of arc CD.

Solution:

Let O be the center of the circle.

In triangle OCD,

[tex]OC=7[/tex]            (Given)

[tex]OC=OD=7[/tex]          (Radii of same circle)

[tex]CD=7[/tex]            (Given)

Since [tex]OC=CD=OD[/tex] all sides are equal, therefore, the triangle OCD is an equilateral triangle.

Measure of each angle of an equilateral triangle is 60 degrees. So,

[tex]m\angle COD=60^\circ[/tex]

The measure of central angle is equal to the measure of corresponding arc.

[tex]m(arcCD)=m\angle COD[/tex]

[tex]m(arcCD)=60^\circ[/tex]

Therefore, the measure of arc CD is 60 degrees.

Answer:

[tex]\frac{y}{8}[/tex]

Step-by-step explanation:

quotient means division

the / means divide

Answer:

y/8

Step-by-step explanation:

quotient means divide, so y divided by 8, or y/8

Given:

The function is

[tex]f(x)=x^3-2[/tex]

The secant line passing through (-4,f(-4)) and (2,f(2)).

To find:

The equation of the secant line.

Solution:

We have,

[tex]f(x)=x^3-2[/tex]

At x=-4,

[tex]f(-4)=(-4)^3-2[/tex]

[tex]f(-4)=-64-2[/tex]

[tex]f(-4)=-66[/tex]

At x=2,

[tex]f(2)=(2)^3-2[/tex]

[tex]f(2)=8-2[/tex]

[tex]f(2)=6[/tex]

The secant line passes through the points (-4,-66) and (2,6). So, the equation of the secant line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-66)=\dfrac{6-(-66)}{2-(-4)}(x-(-4))[/tex]

[tex]y+66=\dfrac{6+66}{2+4}(x+4)[/tex]

[tex]y+66=\dfrac{72}{6}(x+4)[/tex]

On further simplification, we get

[tex]y+66=12(x+4)[/tex]

[tex]y+66=12x+48[/tex]

[tex]y=12x+48-66[/tex]

[tex]y=12x-18[/tex]

Therefor, the equation of the secant line is [tex]y=12x-18[/tex].

Answer:The median number of hours is between 5 and 9

Step-by-step explanation:

The median number of hours students in the class read last week is between 5 and 9

The steps are as follow:

0-4;20

5-9;24  32th median

10-14;10

15-19;4

20-24;2

25-29;3    ∑ = 63 i.e. odd

M = 1/2 (63+1) = 32th observation

So the median number of hours students in the class read last week is between 5 and 9

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Answer:

No Solution

Step-by-step explanation:

Keep in mind that if the grouping isn't right, then my result will be wrong:

-1/2x-(1/2x+4)+12=17x-6(3x+5/6)

Let me just change the formatting for convenience, and then begin the calculations:

[tex]-\frac{1}{2}x-\left(\frac{1}{2}x+4\right)+12=17x-6\left(3x+\frac{5}{6}\right)\:[/tex]

[tex]-\frac{1}{2}x-\frac{1}{2}x-4+12=17x-18x-5[/tex]

[tex]-2\cdot \frac{1}{2}x-4+12=17x-18x-5[/tex]

[tex]-x-4+12=17x-18x-5[/tex]

[tex]-x+8=17x-18x-5[/tex]

[tex]-x+8=-x-5[/tex]

[tex]-x=-x-13[/tex]

[tex]0=-13[/tex]

Result: No Solution

Answer:

22is answer

f (x) = 5x -3

f (5) =5×5-3=25-3=22

Answer:

5

Step-by-step explanation:

f(x)=5x−3

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n  is nax^n−1 .

5x^1−1

Subtract 1 from 1.

5x^0

For any term t except 0, t^0 =1.

5×1

For any term t, t×1=t and 1t=t.

5

Answer:

The gross pay for the week is $701.32

Step-by-step explanation:

J.B. earns $16.60 per hour, and half of it ($16.60/2) for each hour worked over the 8th-hour range.

On the first day, he works 8.25 hours.

We have 8 hours, plus 0.25 hours past the limit, then for the first day he wins:

8*$16.60 + 0.25*($16.60/2) = $134.86

On the second day, he works again 8.25 hours, so he wins the same amount $134.86

On the third day, he works 9.5 hours, then:

We have 8 hours plus 1.5 hours past the limit, then for this day he wins:

8*$16.60 + 1.5*$16.60/2 = $145.25

On the fourth day, he works 11.5 hours, then:

We have 8 hours plus 3.5 hours pást the limit, then for this day he wins:

8*$16.60 + 3.5*$16.60/2 = $161.85

For the last day, he works 7.25 hours, (in this case, we do not have hours worked over the 8-hour limit) then this day he wins:

7.25*$16.60 = $124.50

The gross pay for this week will be equal to:

G = $134.86 + $134.86 +  $145.25 + $161.85 + $124.50 = $701.32

Answer:

a = 9, c = -4?

Step-by-step explanation:

i think these are the two equations, let me know if i'm wrong

2a + 3c = 5; a + 2c = 1

rearrange second equation : a = -2c +1

plug in:

2(-2c +1) +3c = 5

-4c +1 +3c = 5

-c +1 = 5

-c = 4

c = -4

a + 2(-4) = 1

a - 8 = 1

a = 9

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

[tex]A = \frac{1}{2}[/tex]

[tex]B = \frac{2}{3}[/tex]

The product:

[tex]A * B = \frac{1}{2} * \frac{2}{3}[/tex]

[tex]A * B = \frac{1}{1} * \frac{1}{3}[/tex]

[tex]A * B = 1 * \frac{1}{3}[/tex]

[tex]A * B = \frac{1}{3}[/tex]

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

[tex]A = \frac{1}{2}[/tex]

[tex]B = \frac{2}{3}[/tex]

The quotient:

[tex]A / B = \frac{1}{2} / \frac{2}{3}[/tex]

Express as product

[tex]A / B = \frac{1}{2} / \frac{3}{2}[/tex]

[tex]A / B = \frac{1*3}{2*2}[/tex]

[tex]A / B = \frac{3}{4}[/tex]

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

[tex]x = \frac{1}{2}[/tex]

[tex]y = \frac{2}{3}[/tex]

The sum:

[tex]x + y = \frac{1}{2} + \frac{2}{3}[/tex]

Take LCM

[tex]x + y = \frac{3+4}{6}[/tex]

[tex]x + y = \frac{7}{6}[/tex]

Proved, because 7/6 is rational

The above proof works for all values of A, B, x and y; as long as they are rational values

Answer:

(a) 3x+28+5x+52+2x-10=180 (∠ sum of Δ)

                          10x+70=180

                                 10x=110

                                     x=11

(b) ∠C = 2x-10

           = 2(11)-10

           =  12°

Answer:

3/15, 1/5, or 0.2 probability. Highly unlikely

Explanation:

12/15 is the shown probability. The leftover is 3/15, so 3/15 is the chance of missing the basket.

~Hope this helps~