Multiply the polynomials (7a – 7) and (2a2 – a + 5). Simplify the answer. Show your work.

Answer:

B

Step-by-step explanation:

We can use the logarithm property shown below to evaluate this:

[tex]Log(x*y*z)=logx+logy+logz[/tex]

Now we can write Log 12 as Log (2*2*3).

Using the rule, we can write:

Log (2*2*3) = Log 2 + Log 2 + Log 3

We are given values of Log 2 and Log 3, plugging these we get:

Log (2*2*3) = Log 2 + Log 2 + Log 3

Log (2*2*3) = 0.3010 + 0.3010 + 0.4771 = 1.0791

Answer choice B is right.

We can factor out 12 using 2 and 3.

log(12) = log(2^2 * 3)

Rewrite it using the product rule [ log(xy) = log(x) + log(y) ]

log(2^2 * 3) = 2 log(2) + log(3)

Simplify using the given values.

2(0.3010) + 0.4771

0.602 + 0.4771

1.0791

Therefore, the answer is b. ≈ 1.0791

Best of Luck!

Answer:

380.13 m

Step-by-step explanation:

You first need to write down the Area formula for a circle which is  A=pi x radius^2 .

So 11^2 x 3.1415...

121 x 3.1415... = 380.13 m

you got everything right

[tex]\begin{cases}4x - y = 16 \\2x + 3y = - 2 \end{cases} \\ \Leftrightarrow \begin{cases}4x - y = 16 \\4x + 6y = - 4 \end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{y + 16}{4} \\7y = - 20 \end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{23}{7} \\y = - \frac{20}{7} \end{cases}[/tex]

Maybe you wrote the system wrong somewhere because there is no right answer

Answer:

460

Step-by-step explanation:

I=P x r x t

P is the principal amount, $2300.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 4....year(s) time periods.

So, t is 4....year time periods.

To find the simple interest, we multiply 2300 × 0.05 × 4 to get that:

The interest is: $460.00

Answer:

49 units

Step-by-step explanation:

10.50u ≥ 200 + 6.40u       solve for u....

4.10u ≥ 200        (subtract 6.40u to both sides)

       u ≥ 200/4.10  (divide both sides by 4.10)

         u ≥ 48.78

         Any number of units greater than 48.78, but they can't sell parts of a unit, so 49 is the minimum number of units that need to be sold to make a profit  

Answer:

16.51

Step-by-step explanation:

In a parallelogram, the opposite angles are always equal in measure. So two of the angles in the parallelogram measure 39 degrees each.

The sum of angles of the parallelogram must be 360 degrees. Let the other two angles be x degree each. We can set up the following equation for the angles:

39 + 39 + x + x = 360

78 + 2x = 360

2x = 282

x = 141

This means, the other two angles measure 141 degree each. The shorter diagonal will be opposite to the shorter angle.

Hence, the diagonal opposite to the angle 39 degree will be the shorter one. A diagonal divides the parallelogram in two triangles. So we will have two sides and an included angle and we have to find the third side of the triangle which can be found using the law of cosines. Let the third side be c as shown in image below, using the law of cosines, we can write:

[tex]c^{2} = a^{2}+ b^{2} -2ab cos(\gamma)\\\\c^{2}=18^{2}+26^{2}-2(18)(26)cos(39)\\\\ c^{2}=272.59\\\\ c=16.51[/tex]

Thus the shorter diagonal will be 16.51 feet in measure.

To find the shorter diagonal of a parallelogram with given side lengths and angle, use the formula √(a^2 + b^2 - 2abcosθ).

To find the shorter diagonal of a parallelogram, we need to use the formula:

Shorter diagonal = √(a^2 + b^2 - 2abcosθ)

Where a and b are the sides of the parallelogram and θ is the angle between them.

Using the given information, we have a = 18 ft, b = 26 ft, and θ = 39°.

Substituting these values into the formula, we get:

Shorter diagonal = √(18^2 + 26^2 - 2(18)(26)cos(39°))

Calculating this expression gives us:

Shorter diagonal ≈ 9.15 ft

Answer:

the answer is 119g

Step-by-step explanation:

x-120/4.3=-0.25

x-120=-1075

x=118.925=119g

Approximately 40% of the tomatoes weigh less than 119 g.

The correct answer is option D.

A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.

It measures the unusual or extreme a particular data point is compared to the rest of the distribution

We have,

To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.

The CDF gives the probability that a random variable is less than or equal to a given value.

Given that the mean of tomato weight is 120 grams and the standard deviation is 4.3 grams,

We can use this information to find the probability that a randomly selected tomato weighs less than a certain amount.

Let's calculate the z-score for each option:

A. 111 g:

z-score = (111 - 120) / 4.3 ≈ -2.093

B. 114 g:

z-score = (114 - 120) / 4.3 ≈ -1.395

C. 117 g:

z-score = (117 - 120) / 4.3 ≈ -0.698

D. 119 g:

z-score = (119 - 120) / 4.3 ≈ -0.233

Now, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) of the standard normal distribution to find the probability corresponding to each z-score.

The option with the highest probability, or approximately 40%, is the correct answer.

Based on the calculations, it appears that option D. 119 g has the highest probability of approximately 40% for a tomato weighing less than that amount.

Thus,

Approximately 40% of the tomatoes weigh less than 119 g.

Learn more about z-score here:

https://brainly.com/question/15016913

#SPJ3

Answer:

Step-by-step explanation:

(a) when there is a negative in front of the leading coefficient  (- x^2), that is a reflection over the x axis.  a regular parabola opens up.  In this case, the negative in front of the first term makes it open downward.  

-f(x) is a reflection    so -2x^2 would open downward.

(b) the vertex of the parabola is -b/2a

in this problem a x^2 + bx + c = y

                         -2x^2 + 4x + 3 = y

a = -2, b = 4, c = 3

formula for vertex -b/2a  = -4/2(-2)    = -4/-4  = 1    This is the x-value of the vertex.  Plug back into original equation to find the y value.

(1, ?)    -2(1)^2 + 4(1) + 3 = 5

vertex is (1,5) and is above the x axis

Answer:

Step-by-step explanation:

Left Frame

Consecutive angles (angles that are one after another) add up to 180 degrees. (The are supplementary).

9x + 6x = 180o               Combine like terms

15x = 180o                      Divide by 15

15x/15 =180/15

x = 12

===============

You could do this the way it is done in the more formal proof.

9x + 6x + 9x + 6x = 360     Combine like terms: each quadrilateral = 180o

30x = 360                            Perform Division Property of equality

x = 360/30                           Do the division

x = 12

Right frame

The left side of line 3 is the substitution property.

<A = 9x

<B = 6x

<C = 9x

<D = 6x

The left side of line 4 is 30x. This comes from 9+6 + 9 + 6

The right side of line 5 is the division property of equality

Answer:

the pdf wnt lad gimme dem pons doe

Step-by-step explanation:

Answer:

1 1/4

Step-by-step explanation:

rigjt answer

Answer: option a.

Step-by-step explanation:

To solve the given exercise nad write the expression as a single logarithm, you must keep on mind the following properties:

[tex]ln(a)+ln(b)=ln(ab)\\m*ln(a)=ln(a)^m[/tex]

Therefore, by applying the properties shown above, you can rewrite the expression given, as following:

[tex]lnx^{2}+3lny=lnx^2+lny^3=ln(x^2y^3)[/tex]

Then, the answer is the option a.

Answer:

b. [tex]x=\frac{5\pi}{6}[/tex]

Step-by-step explanation:

The given function is

[tex]\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi[/tex]

Recall that the reciprocal of the cosine ratio is the secant ratio.

This implies that;

[tex]\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}[/tex]

[tex]\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }[/tex]

[tex]\Rightarrow \cos x=-\frac{\sqrt{3}}{2}[/tex]

We take the inverse cosine of both sides to obtain;

[tex]x=\cos^{-1}(-\frac{\sqrt{3}}{2})[/tex]

[tex]x=\frac{5\pi}{6}[/tex]

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - height

We have r = 1cm and H = 21cm. Substitute:

[tex]V=\pi(1^2)(21)=21\pi\ cm^3[/tex]

The formula of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have V = 21π cm³ and H = 7cm. Substitute:

[tex]\dfrac{1}{3}\pi(r^2)(7)=21\pi[/tex]        divide both sides by π

[tex]\dfrac{1}{3}(7)(r^2)=21[/tex]         divide both sides by 7

[tex]\dfrac{1}{3}r^2=3[/tex]         multiply both sides by 3

[tex]r^2=9\to r=\sqrt9\\\\r=3\ cm[/tex]

Answer:

A 3cm

Step-by-step explanation:

Answer: option b.

Step-by-step explanation:

To solve the given exercise, you must keep on mind the following law of logaritms:

[tex]m*log(a)=log(a)^m[/tex]

Descompose 8 into its prime factors:

[tex]8=2*2*2=2^3[/tex]

Therefore,  you can rewrite the expression given, as following:

[tex]log8=log2^3=3log2[/tex]

You know that [tex]log2=0.3010[/tex]

Then, when you substitute, you obtain:

[tex]3*0.3010[/tex]≈0.9030

Factor out 8 using 2.

log(8) = log(2^3)

Use the product rule [ log(xy) = log(x) + log(y) ] to simplify.

log(2^3) = 3 log(2)

Simplify using the given value for 2.

3(0.3010)

0.9030

Therefore, log(8) ≈ 0.9030 (Option B)

Best of Luck!

Answer:

  P = 10x³ + 4x² + 8x + 6

Step-by-step explanation:

The perimeter of a rectangle is twice the sum of length and width.

  P = 2(L+W) = 2((x³ +2x² -6x +12) +(4x³ +10x -9))

  = 2(5x³ +2x² +4x +3) . . . . collect terms inside parentheses

  P = 10x³ +4x² +8x +6

Final answer:

Each person will get 1 cookie and there will be 3 cookies leftover.

Explanation:

In this scenario, we have 7 cookies that are being shared equally among 4 people. To find out how many cookies each person will get, we divide the total number of cookies by the number of people.

So, 7 cookies divided by 4 people = 1.75 cookies per person.

Since we can't divide a cookie into fractions, each person will get 1 cookie and there will be 3 cookies leftover.

Your room temperature is 25°C.

Step-by-step explanation:

hope this helps!

Answer:

The y-coordinate of the y-intercept is [tex]-4[/tex]

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

[tex]F(x)=-3x^2+5x-4[/tex]

Find the y-intercept

For [tex]x=0[/tex]

[tex]F(0)=-3(0)^2+5(0)-4=-4[/tex]

The y-intercept is the point [tex](0,-4)[/tex]

therefore

The y-coordinate of the y-intercept is [tex]-4[/tex]

Answer:

The value would be -4.

Step-by-step explanation:

Step-by-step explanation:

4/5x+5<-3

4/5x<-8

4x<-40

x<-10

The original width was 6 inches, the new width is 9 inches.

Divide the new width by the original width to find the scale factor:

9/6 = 1.5

Now multiply the original height by the scale factor to find the new height:

4 x 1.5 = 6 inches.

Answer: step 3

I just took the test and got a 100%

Answer:

Step 3

Step-by-step explanation:

Here, the given expression,

[tex]7b + 3.2b - 5 = 18.92[/tex]

Since, when we solve the given expression the steps of solution are as follows,

Step 1 : 7b + 3.2b - 5 = 18.92

Step 2 : 10.2b - 5 = 18.92      ( Combining like terms in left side )

Step 3 : 10.2b = 23.92           ( Adding 5 on both sides )

Step 4 : b = 4.6                       ( Dividing both sides by 10.2 )

Hence, by the above explanation it is clear that she made her mistake in step 3 ( she did not add 5 on right side )

ANSWER

5.5

EXPLANATION

We can use the cosine rule to find the missing side length.

The cosine rule is given as;

[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos( A) [/tex]

Let the missing side be "a".

Then,

[tex] {a}^{2} = {9}^{2} + {6}^{2} - 2 \times 9 \times 6 \cos(37 \degree) [/tex]

[tex] {a}^{2} = 81+ 36- 86.253[/tex]

[tex] {a}^{2} = 30.74736[/tex]

[tex]a = \sqrt{30.747} [/tex]

[tex]a \approx5.5[/tex]

Therefore the missing side length is approximately 5.5 units to the nearest tenth.

Answer:

Option C [tex]9\ sandwiches[/tex]

Step-by-step explanation:

we know that

using proportion

[tex]\frac{1}{(1/3)}\frac{sandwich}{pounds}=\frac{x}{3}\frac{sandwiches}{pounds}\\ \\x=3*3\\ \\x=9\ sandwiches[/tex]

Answer:

9

Step-by-step explanation:

I got the answer from USATestprep

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=7850 \end{cases}\implies 7850=2\pi r\implies \cfrac{7850}{2\pi }=r\implies 1249.37\approx r[/tex]

Answer:

1249.37 units

Step-by-step explanation:

[tex]x - |-20| = |-34|\\x-20=34\\x=54[/tex]

ANSWER

The height of the square pyramid is 4.8m

EXPLANATION

The volume of a square pyramid is calculated using the formula:

[tex]Volume = \frac{1}{3}(base \: area) \times height[/tex]

It was given that;

The volume of the square pyramid is

[tex]25 \frac{3}{5} {m}^{3} [/tex]

The side length of the square base is

[tex]4m[/tex]

We substitute the given values and then solve for the height.

[tex]25 \frac{3}{5} = \frac{1}{3}( {4}^{2} ) \times height[/tex]

We solve for the height to obtain;

[tex]height = \frac{25 \frac{3}{5} }{ \frac{16}{3} } [/tex]

We simplify to get;

[tex]height = 4.8m[/tex]

Hence, the height of the square pyramid is 4.8 meters.

Answer:

The height of the square pyramid is 4.8 meters.

Step-by-step explanation:

I just know

Answer:

a) 7069.82 Liters

b) 600 seconds

c) Shown below

d) (i) 0.6935 liters   (ii)  Since 0.6935 liters in 0.001 minute, so 693.5 liters per minute is as estimate (in liters per minute)

Step-by-step explanation:

a)

We simply put 5 into t of the equation and get the value of V. So:

[tex]V=10,000(0.933)^t\\V=10,000(0.933)^5\\V=7069.82[/tex]

So after 5 minutes the amount remaining is 7069.82 Liters

b)

half of the initial amount is half of 10,000 which is 5000. So we substitute 5000 into V and solve for t using logarithms.

Note: [tex]ln(a^b)=blna[/tex]

Thus, we have:

[tex]V=10,000(0.933)^t\\5000=10,000(0.933)^t\\0.5=(0.933)^t\\ln(0.5)=ln((0.933)^t)\\ln(0.5)=tln(0.933)\\t=\frac{ln(0.5)}{ln(0.933)}\\t=9.99[/tex]

Thus, t = 9.9949 minutes.

To get answer in seconds, we multiply by 60. Thus 9.9949*60= 600 seconds

c)

95% empty means 5% remaining. 5% of 10,000 = 0.05 * 10,000 = 500. We plug in 500 into V and solve for t as the previous step. Shown below:

[tex]V=10,000(0.933)^t\\500=10,000(0.933)^t\\0.05=0.933^t\\ln(0.05)=ln(0.933^t)\\ln(0.05)=tln(0.933)\\t=\frac{ln(0.05)}{ln(0.933)}\\t=43.1972[/tex]

So it takes around 43.1972 minutes to empty 95%. Since three-quarters of an hour is  [tex](\frac{3}{4})(60)=45[/tex] minutes, we have shown that the time it takes (43.1972 minutes) is very close to three-quarters of an hour.

d)

We plug in 0.001 into t and find V. Then we subtract that value from 10,000. This is just finding how much water has been removed in 0.001 minutes. Let's do this:

[tex]V=10,000(0.933)^t\\V=10,000(0.933)^{0.001}\\V=9999.3065\\Now\\10,000 - 9999.3065 = 0.6935[/tex]

So, 0.6935 liters

Answer:

[tex]\$103.75[/tex]

Step-by-step explanation:

step 1

Find the area of the gate

The area of the gate is equal to the area of a trapezoid minus the area of the rectangular glass panel

[tex]A=\frac{1}{2}(10+7)(5)-(0.71)(1.43)= 41.5\ ft^{2}[/tex]

step 2

Find the cost

Multiply the total area by $2.50  

so

[tex]41.5*2.50=\$103.75[/tex]

Answer:

1. B 2. C

Step-by-step explanation:

1. B is the answer because if you add 8 times 1 to 11 you get 19 and if you add 8 times 2 to 11 you get 27 so that is the expression to represent the pattern.

2. C is the answer because if you add -9 times 1 to 80 you get 71 and if you add -9 times 2 to 80 you get 62 so that is the expression to represent the pattern.