A recipe calls for 1/3/4 cups of sugar. The recipe requires 3/4 cup more flour than sugar and 1/2 cup less butter than sugar.

givi [52]

Answer:

There are 6*5*4 = 120 possible 3-digit numbers, of which 60 must be even and 60 must be odd, since there are 3 even possible ending digits and 3 odd possible ending digits.

Step-by-step explanation:

7 0

3 years ago

Quick Math, Please Help! Thank you!

lesantik [10]

Answer:

The remaining side has a length of six units.

Step-by-step explanation:

We know that this is an Isosceles triangle because angles A and C are marked as being the same angle. So we know that AB and CB are the same length.

As we're given their lengths, we can simply equate the two, and solve for x:

$x + 4 = 3x - 8\\12 = 2x\\x = 6$

So we know that the remaining side has a length of 6.

5 0

2 years ago

Read 2 more answers

Find all the zeros of the equation x^4-6x^2-7x-6=0

rusak2 [61]

Answer:

The zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

$a_0=6,\:\quad a_n=1$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\$

$=x^3-2x^2-2x-3$

Again factor using the rational root test, we get

$=\left(x+2\right)\left(x-3\right)\left(x^2+x+1\right)$

Using the zero product rule, we have

$x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Therefore, the zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

4 0

3 years ago

Read 2 more answers

PLEASE HELP!!

artcher [175]

To solve for f, you need to isolate/get the variable by itself in the equation:

4(0.5f - 0.25) = 6 + f Distribute 4 into (0.5f - 0.25)

(4)0.5f + (4)(-0.25) = 6 + f

2f - 1 = 6 + f Subtract f on both sides to get "f" on one side of the equation

2f - f - 1 = 6 + f - f

f - 1 = 6 Add 1 on both sides to get "f" by itself

f - 1 + 1 = 6 + 1

f = 7

PROOF

4(0.5f - 0.25) = 6 + f Substitute/plug in 7 into "f" since f = 7

4(0.5(7) - 0.25) = 6 + 7

4(3.5 - 0.25) = 13

4(3.25) = 13

13 = 13

8 0

3 years ago

A driver drove for 3 hours at a certain speed. If he drove 12 more miles at the same speed, the distance would be 132 miles. At

Zinaida [17]

Distance traveled in 3 hrs was (speed in mph)(3 hrs)

Then s(3 hrs) + 12 mi = 132 mi.

Therefore, 3s = 120, and s = 120 miles / 3 hrs = 40 mph (answer)

7 0

2 years ago