Which of the following are expressions? Check all that apply.



Group of answer choices

3 + x

twelve is three more than nine

the difference of x and 8

2y

Answer:

31°

Step-by-step explanation:

<Y + <X = 180° [being co-interior angles ]

s + 91° + 2s - 4° = 180°

3s + 87° = 180°

3s = 180° - 87°

3s = 93°

s = 93° /3

s = 31°

Hope it will help you :)❤

Answer:

\(\displaystyle 31\)

Step-by-step explanation:

Angles Y and X form a linear pair, therefore you use the Linear Pair Theorem to solve for x:

\(\displaystyle 180° = [2s - 4]° + [s + 91]° → 180° = [87 + 3s]° → 93 = 3s; 31 = s\)

I am joyous to assist you at any time.

So,

Here we have the following quadratic equation:

We're going to solve it by completing the square.

What we do, is to get a binomial of the form:

Adding and substracting a number to the equation.

In this case, you can notice that:

Rewriting:

Therefore, the equation (x + 7 )^2 = 34 shows an accurate step in the process.

Answer:

x = 22

3x + 2 = 68°

Step-by-step explanation:

x + 3x + 2 = 90° because this is a right triangle

3x + 2 = 90

4x = 88 divide by 4

x = 22

3x + 2 replace x with the value we found

3×22 + 2 = 68°

3 Since the smaller photo has a decrement ratio of roughly $3 to $6, it would be half as tall in Diagram 1, making it 2 inches wide. For Diagram 1, the height is 6 for the usual photo, therefore each one has to be 3 inches high.

To learn more about ratio, refer to:

https://brainly.com/question/2328454

#SPJ1

Answer: m = -1/2

Use (y2-y1)/(x2-x1) to find the slope.

Given the information on the table, we can find out the constant of variation by working a few cases:

Therefore, k=4. To find the equation we simply solve for y the first equation:

Finally, the equation is y=4x

Approximately 94.90% of the men in the country are eligible for the military based on height.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z-score = (X-ц )/σ

First, we need to standardize the values of 66 and 77 using the given mean and standard deviation:

Z(66) = (66 - 70.4) / 2.6 = -1.69

Z(77) = (77 - 70.4) / 2.6 = 2.54

The percentage of the area under the standard normal distribution curve is between -1.69 and 2.54.

Using a standard normal distribution table, we can find that the area to the left of Z = -1.69 is 0.0455 and the area to the left of Z = 2.54 is 0.9945.

Therefore, the area between Z = -1.69 and Z = 2.54 is:

0.9945 - 0.0455 = 0.9490

This means that approximately 94.90% of the men in the country have heights between 66 inches and 77 inches.

Learn more about the z-score here:

brainly.com/question/13793746

#SPJ1

Answer:

Step-by-step explanation:

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Learn more about modular equation click here:

https://brainly.com/question/15055095

#SPJ1

Answer:

144

Step-by-step explanation:

6^2 = 6x6 = 36

36 x 4 = 144

Answer: 60 pages

Step-by-step explanation: 24 pages time 2 would be 48 pages, which is 80% of the pages. Since 12 pages is 20%, you would add 12 pages, which equals 60 pages.

The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

learn more on arc angle here: https://brainly.com/question/22826189

#SPJ1

Answer:

It's in the attachment

hope it helps...

have a great day!!

Answer:

option b

Step-by-step explanation:

x is greater than or equal to 66

Answer:

Option B

Have a nice day! :)

The value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

The quadratic equation is given as:

–3 = –x^2 + 2x

Rewrite the equation as:

x^2 - 2x - 3 = 0

A quadratic equation is represented as;

ax^2 + bx + c = 0

So, we have

a = 1

b = -2

c = -3

The discriminant is

d = b^2 - 4ac

So, we have

d = (-2)^2 - 4 * 1 * -3

Evaluate

d = 16

Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

Read more about quadratic equation a

https://brainly.com/question/1214333

#SPJ1

Answer:

16

Step-by-step explanation:

Answer:

O a=0

Step-by-step explanation:

Answer:

ay

Step-by-step explanation: step by step

On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.03357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

To know more about surface area visit:

brainly.com/question/2835293

#SPJ1

\(\dfrac{5 \sin 87^{\circ} + \tan 72^{\circ} - \sec 5^{\circ}}{\cot 18^{\circ}-\csc 85^{\circ}+5\cos 3^{\circ}}\\\\\\=\dfrac{5\sin\left(90^{\circ}-3^{\circ} \right) + \tan\left(90^{\circ}-18^{\circ} \right)-\sec\left(90^{\circ}-85^{\circ} \right)}{\cot 18^{\circ}-\csc 85^{\circ}+5\cos 3^{\circ}}\\\\\\=\dfrac{5\cos 3^{\circ} + \cot 18^{\circ}-\csc 85^{\circ}}{\cot 18^{\circ}-\csc 85^{\circ}+5\cos 3^{\circ}}\\\\\\=1\)

We have proved that if ∑aₙ is a conditionally convergent series, then the series ∑(aₙ⁴ + 5ⁿaₙ²) is divergent.

A divergent series is a series that does not have a finite sum, meaning that the partial sums of the series do not converge to a finite limit.

Since ∑aₙ is conditionally convergent, we know that the series ∑aₙ converges but ∑|aₙ| diverges. Let's assume that ∑(aₙ⁴ + 5ⁿaₙ²) converges, then we can apply the limit comparison test to the series ∑(aₙ⁴ + 5ⁿaₙ²) and the series ∑|aₙ|.

Using the limit comparison test, we have:

limₙ→∞ [(aₙ⁴ + 5ⁿaₙ²) / |aₙ|] = limₙ→∞ [|aₙ|⁻³(aₙ⁴ + 5ⁿaₙ²)]

We know that ∑|aₙ| diverges, so we have:

limₙ→∞ [|aₙ|⁻³(aₙ⁴ + 5ⁿaₙ²)] = ∞

Therefore, the limit comparison test implies that ∑(aₙ⁴ + 5ⁿaₙ²) also diverges.

Hence, we have proved that if ∑aₙ is a conditionally convergent series, then the series ∑(aₙ⁴ + 5ⁿaₙ²) is divergent.

To learn more about Divergent Series from the given link

https://brainly.com/question/15415793

#SPJ1

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

learn more on kite here: https://brainly.com/question/27975644

#SPJ9

Using the normal distribution, it is found that there is a 0.6568 = 65.68% probability that the variable that is between −1.33 and 0.67.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, we have a standard normal distribution, hence \(\mu = 0, \sigma = 1\).

The probability that the variable is between −1.33 and 0.67 is the p-value of Z when X = 0.67 subtracted by the p-value of Z when X = -1.33, hence:

X = 0.67

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{0.67 - 0}{1}\)

\(Z = 0.67\)

\(Z = 0.67\) has a p-value of 0.7486.

X = -1.33

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{-1.33 - 0}{1}\)

\(Z = -1.33\)

\(Z = -1.33\) has a p-value of 0.0918.

0.7486 - 0.0918 = 0.6568.

0.6568 = 65.68% probability the variable that is between −1.33 and 0.67.

You can learn more about the normal distribution at https://brainly.com/question/24663213

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

12 + \(4\sqrt{5}\) approximates to 20.944

Step-by-step explanation:

VU - 8 units

UW - 4 units

VW - \(\sqrt{64+16} = \sqrt{80} =4\sqrt{5}\)

12 + 4sqrt(5)

Answer:

6 (2 + √5) units

Step-by-step explanation:

Finding the length of the 3rd side :

*Applying Pythagorean Theorem*

The perimeter :

Answer:

a) The number of claims decrease from 1990 to 1996.

b) The relative extrema is a minimum and happens approximately in 1996 (t=5.688). This means the moment when the number of claims stop decreasing and start to increase.

Step-by-step explanation:

The monthly average number of unemployment claims in a certain county is given by:

\(C(t)=24.31t^2-276.58t+2035\)

With t: number of years after 1990.

We have to determine in what years the number of claims decrease and the relative extreme value.

We can find this by analizing the first derivative.

When the first derivative is equal to zero, this indicates an extreme value, which can be a maximum or minimum.

When the first derivative is positive, it indicates that the function is increasing. On the contrary, when the first derivative is negative, it indicates that the function is decreasing.

The first derivative is:

\(\dfrac{dC}{dt}=24.31(2t)-276.58(1)+0\\\\\\\dfrac{dC}{dt}=48.62t-276.58\)

Then, we can calculate the extreme value:

\(\dfrac{dC}{dt}=48.62t-276.58=0\\\\\\48.62t=276.58\\\\\\t=\dfrac{276.58}{48.62}=5.688\approx 6\)

This extreme value happens for t=6 (year 1996).

If we calculate the value of the first derivative for t=5, that is previous to the extreme value, we can find if the function was increasing or decreasing:

\(\dfrac{dC}{dt}(5)=48.62*5-276.58=243.10-276.58=-33.48<0\)

As the value is  negative, we know that the number of claims was decreasing from t=0 to t=6 (from 1990 to 1996), and then reach a minimum and start to increase from them (from 1996 onwards).

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Using the concept of proportion, amount of gas needed to travel 250 miles is 9.5 gallons.

Given that,

Ms C's car uses 20 gallons of gas to travel 400 miles.

We have to first find the number of gallons of gas to be used to travel 250 miles.

Amount of gas used to travel 400 miles = 20 gallons

Using the concept of proportion,

Amount of gas used to travel 1 mile = 20 / 400

                                                           = 0.05 gallon

Amount of gas used to travel 250 miles = 0.05 × 250

                                                                  = 12.5 gallons

There is already 3 gallons of gas in her car.

Amount of gas needed = 12.5 - 3 = 9.5 gallons

Hence the amount of gas needed is 9.5 gallons.

Learn more about Proportions here :

https://brainly.com/question/30675547

#SPJ1