In parallelogram DEFG, DH = x + 2 HF = 2y, GH = 4x-3 and HE = 4y + 1. Find the values of x and y. The diagram is not drawn to scale.

ANSWER

[tex]log_{15}( {2}^{3} ) = 3 \: log_{15}( {2} )[/tex]

EXPLANATION

According to the power property of logarithms:

[tex] log_{x}( {y}^{n} ) = n \: log_{x}( {y} )[/tex]

The given logarithm is

[tex]log_{15}( {2}^{3} ) [/tex]

When we apply the power property to this logarithm, we get,

[tex]log_{15}( {2}^{3} ) = 3 \: log_{15}( {2} )[/tex]

Answer:

The required expression is [tex]3\log_{15}2[/tex].

Step-by-step explanation:

According to the power property of exponent,

[tex]\log_ax^b=b\log_ax[/tex]

The given expression is

[tex]\log_{15}2^3[/tex]

Here a=15, x=2, b=3.

Using power property of exponent the given expression can be written as

[tex]\log_{15}2^3=3\log_{15}2[/tex]

Therefore the required expression is [tex]3\log_{15}2[/tex].

The correct option is C.

Probability of selecting all boys from 8 boys and 6 girls for a 4-person committee is 10/143.

To find the probability that the committee consists of all boys, we need to calculate the probability of selecting 4 boys out of 8 boys and no girls out of 6 girls.

The total number of ways to choose a 4-person committee from 14 students (8 boys and 6 girls) is given by the combination formula:

[tex]\[ \text{Total number of ways} = \binom{14}{4} \][/tex]

The number of ways to choose 4 boys out of 8 is given by:

[tex]\[ \binom{8}{4} \][/tex]

And since we don't choose any gi-rls, the number of ways to choose 0 girls out of 6 is simply 1.

So, the probability of selecting all boys is:

[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} \][/tex]

Let's calculate this:

[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} = \frac{\frac{8!}{4!(8-4)!} \times \frac{6!}{0!(6-0)!}}{\frac{14!}{4!(14-4)!}} \][/tex]

[tex]\[ = \frac{\frac{8!}{4!4!} \times 1}{\frac{14!}{4!10!}} \][/tex]

[tex]\[ = \frac{\frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}}{\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}} \][/tex]

[tex]\[ = \frac{70}{1001} \][/tex]

[tex]\[ = \frac{10}{143} \][/tex]

So, the correct answer is option C: [tex]\( \frac{10}{143} \)[/tex].

The complete question is here:

A four-person committee is chosen from a group of eight boys and six girls.. If students are chosen at random, what is the probability that the committee consists of all boys?

A. 4/1001

B. 15/1001

C. 10/143

D. 133/143

Answer:

...

Step-by-step explanation:

can you show us the options of the drop-down menus?

C. the number goes up by one tenth. changing the 0 in the tenth place to a one.

Your answer would be

c. 5.123 since

5.023

+0.1

————

5.123

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (-3,2)~~ \begin{cases} x=-3\\ y=2 \end{cases}\implies 2=k(-3)\implies -\cfrac{2}{3}=k[/tex]

To find the constant of variation k in the direct variation y = kx for the point (–3, 2), we substitute the point into the equation.

We get k = 2 / (–3), resulting in k = –rac{2}{3}.

The constant of variation, k, in the direct variation equation y = kx can be found using the coordinates of a given point that lies on the line represented by this equation.

Given a point (–3, 2), we can substitute these values into the equation to find k:

y = kx

2 = k(–3)

To isolate k, we divide both sides of the equation by (–3):

k = 2 / (–3)
k = –rac{2}{3}

Answer: 16/25

4/10 divided by 5/8 = ?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal or inverse of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes -

4/10 x 8/5 = ?

For fraction multiplication, multiply the numerators and then multiply the denominators to get -

Numerators: 4 x 8 = 32

Denominators: 10 x 5 = 50

Fraction: 32/50

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 32 and 50. The GCF (Greatest Common Factor) would be 2.

Numerator: 32 / 2 = 16

Denominator: 50 / 2 = 25

Fraction: 16/25

4/10 divided by 5/8 = ?

Cross multiply -

Numerator x Denominator: 4 x 8 = 32

Denominator x Numerator: 10 x 5 = 50

Fraction: 32/50

Reduce by dividing both the numerator and denominator by the Greatest Common Factor, which is 2.

Numerator: 32 / 2 = 16

Denominator: 50 / 2 = 25

Fraction: 16/25

Volume of the sphere is defined as: [tex]V=\frac{4\pi r^3}{3}[/tex]

Put in the data.

[tex]V=\frac{4\cdot3.14\cdot3^3}{3}=\boxed{113.04}[/tex]

The point on the number line of real numbers is 113.04

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

[tex]x=180-(51+62)=180-113=\boxed{67}[/tex]

Answer:

x = 67

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 to obtain x, that is

x = 180° - (62 + 51)° = 180° - 113° = 67°

Answer:

Amount invested at 8% = $2800

Amount invested at 5.5% = $2200.

Step-by-step explanation:

Let the amount invested at 8% = x

Then the amount invested at 5.5% = 5000-x

Then we get equation:

[8% of x] + [5.5% of (5000-x)] = [6.9% of 5000]

8(x) + 5.5(5000-x) = 6.9(5000)

8x + 27500 - 5.5x = 34500

8x - 5.5x = 34500-27500

2.5x = 34500-27500

2.5x = 7000

x = 7000/2.5

x = 2800

then  the amount invested at 5.5% = 5000-x = 5000-2800 = 2200

Hence final answer is given by:

Amount invested at 8% = $2800

Amount invested at 5.5% = $2200.

Answer:

A

Step-by-step explanation:

This one is best done by doing a pre factor.

140 = 14 * 10 Now all you need do is factor those two numbers.

140 = 7*2 * 5 * 2

Rearranging this you get 2 * 2 * 5 *7

A

Final answer:

The prime factorization of 140 is found by dividing it by the prime numbers 2, 2, 5, and 7 in sequence, resulting in 2 x 2 x 5 x 7, which corresponds to option A.

Explanation:

The prime factorization of a number is the expression of the number as a product of its prime factors. To find the prime factorization of 140, we can use a factor tree or continuously divide by prime numbers. Beginning with the smallest prime number, 2, we divide 140 by 2 to get 70. Then, we divide 70 by 2 again to get 35. After that, we divide 35 by its smallest prime factor, which is 5, to get 7. Since 7 is already a prime number, we have completed the factorization. So, the prime factorization of 140 is:

2 x 2 x 5 x 7

Therefore, the correct answer is A.2 x 2 x 5 x 7.

Answer:

2824

Step-by-step explanation:

Take the number of pounds and divide by the number of people:

3.474×10⁹ / 1.23×10⁶

Divide the coefficients and subtract the exponents:

(3.474 / 1.23) × 10⁹⁻⁶

2.824×10³

So the country produced about 2,824 pounds of garbage per person in 2005.

Answer:

Option A

Step-by-step explanation:

Positive trend will start from bottom to going upwards and negative trend will start from the top to bottom.

Weight and height is also logical because as height goes up, weight will follow up.

Answer:

4

Step-by-step explanation:

Ok, so from what I understand 6+ half of the apples equals 8... so that means there is four apples.

4 divided by 2 = 1/2 which is 2 plus 6 equals 8

This is my first brainly answer!

I hope this is correct and helps! :)

Answer:

x=2

Step-by-step explanation:

(5x–7)–5(7x–12)+7=0

5x-7-35x+60+7=0

-30x=-60

x=2

Answer:

The answer I got was x=2

300/2.5= 120 Calories

Answer:

120 calories

Step-by-step explanation:

Answer:

13cm, 7cm, 6cm

Step-by-step explanation:

To make a triangle you have to think about it in this way. The two smallest numbers should equal the largest number.

Answer:

13 cm, 7 cm, 6 cm

Step-by-step explanation:

The sum of the 2 shorter sides of the triangle has to be equal or longer than the longest side. In this case 7+6=13 which is equal.

Formula for area is:

A = pi*r^2

r = 28

so...

A = 3.14 * 28^2

A = 3.14 * 784

A = 2461.76 cm^2

Formula for circumference is:

C = 2*pi*r

r = 28

so...

C = 2*3.14* 28

C = 6.28*28

C = 175.84 cm

Hope this helped!

~Just a girl in love with Shawn Mendes

It’s > because when you square root 18 it’s 4.24264069

Answer:

The answer would be C, Greater Than, >.

Step-by-step explanation:

In this question, it is asked if 5 is equal to, less than or greater than the square root of 18. So we first need to find out the value of square root 18. We can do it manually or with a scientific calculator. If we do it with a calculator, we would come to know that the answer of square root 18 is 4. 24264068. Now we would compare it with 5. We will have to see if 5 is equal to, less than or greater than this value of square root of 18. So it is clear from the above answer of square root 18, that it is less than 5.

So the answer is C, that shows that 5 is greater than square root of 18, i-e 4.24264068.

Answer with Step-by-step explanation:

A candle is 4 inches tall and burns at the rate of 0.6 inch per hour.

i.e. after 1 hour height of candle=4-0.6 inches

After 2 hours height of candle=4-0.6-0.6 inches

after x hours height of candle=4-0.6x

Also,

If the height of the candle after x hours is 1.5 inches

⇒  4-0.6x=1.5

⇒ 0.6x=4-1.5

⇒ 0.6x=2.5

⇒ x=2.5/0.6

⇒ x=4.166

Hence, equation to represent the situation. is:

4-0.6x=1.5

and the expected number of hours in which the candle  melted to 1.5 inches is:

4.166 hours

After defining and solving the linear equation representing the candle's height over time, it is determined that it will take approximately 4.17 hours for the candle to burn down to 1.5 inches.

This is a problem about rates and linear equations in the subject of mathematics. The candle starts at 4 inches and burns at a rate of 0.6 inch per hour, which decreases the height of the candle. So, the equation would be: height = starting height - (burn rate)x(time), or H = 4 - 0.6x.

From the problem we know, that the height of the candle after x hours is 1.5 inches. So, we substitute H with 1.5: 1.5 = 4 - 0.6x.

To solve for x, first we can subtract 4 from both sides: -2.5 = -0.6x. Then, divide both sides by -0.6 to isolate x. So, x = -2.5/-0.6 which simplifies to approximately 4.17 hours. So, it will take around 4.17 hours for the candle to burn down to 1.5 inches.

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False because x should have only one y

Answer:

Vertex;

(2, -8)

The intercepts;

x-intercepts: (-2, 0) and (6, 0)

y-intercepts: (0, -6)

The axis of symmetry;

No axis of symmetry. X = 2 is a line of symmetry of the parabola

The sign of the lead coefficient;

Positive

Step-by-step explanation:

The graph shown in the attachment belongs to the parabola group of conic sections. The vertex of a parabola refers to the point where the parabola changes direction or also the lowest or the highest point on its graph. The graph is moving downwards from x = -4 to x = 2 and then starts moving upwards from x = 2 to x = 8. The vertex is thus located at the point x = 2. At this point, the y value is -8. Thus the vertex is located at (2, -8). This is the lowest point on the graph.

The intercepts refers to the points where the graph of a function crosses or cuts either the x or the y axes.

The parabola crosses the x-axis at two points;

x = -2 and x = 6

At these points the value of y is usually 0. The x-intercepts are thus;

(-2, 0) and (6, 0)

The parabola crosses the y-axis at the point where y = -6 and the corresponding x value is 0. The y-intercept is thus;

(0, -6)

Neither the x-axis nor the y-axis is an axis of symmetry of the parabola since neither of the axis divides the parabola into two identical portions. Nevertheless, the vertical line x = 2 passing through the vertex divides the parabola into two identical portions such that the left portion is a mirror image of the right portion. We can thus conclude that the vertical line x = 2 is a line of symmetry of the parabola.

The sign of the lead coefficient of a parabola determine whether the parabola opens upward or downward;

If the sign of the lead coefficient is positive, the parabola opens upward. If the sign of the lead coefficient is negative, the parabola opens downward.

The parabola in the attachment opens upward and thus the sign of its lead coefficient is positive.

ANSWER

[tex]x = - 3 \: \: or \: \: x = 3[/tex]

The degree is two so it must have more than one solution.

EXPLANATION

The given equation is

[tex] {x}^{2} = 9[/tex]

Let us use the square root method to solve this equation.

Since the degree of x is two, the fundamental theorem of algebra says it must have 2 roots.

We take square root to obtain,

[tex]x = \pm \sqrt{9} [/tex]

[tex]x = \pm3[/tex]

Split the plus or minus sign to obtain,

[tex]x = - 3 \: \: or \: \: x = 3[/tex]

The solutions to the equation x² = 9 are x = 3 and x = -3. Because squares of both positive and negative numbers give the same result, quadratic equations usually have two solutions.

The solutions to the equation x² = 9 are x = 3 and x = -3. This is because square roots can be both positive and negative. When you square a positive number and a negative number, the result is the same. Hence, the equation x² = 9 could come from squaring either 3 or -3, which implies that x can be either 3 or -3. Therefore, quadratic functions or second-order polynomials, like this equation, usually have two solutions.

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Answer:

Tbh I have no clue..

Answer:

This polynomial can be simplified to a difference of squares

[tex]16a^2 - 4a + 4a - 1=(4a-1)(4a+1)[/tex]

Step-by-step explanation:

Simplify the expression

[tex]16a^2 - 4a + 4a - 1\\\\16a^2- 1[/tex]

remember that 4 ^ 2 = 16

Therefore

[tex]16a^2- 1= 4^2a^2 -1[/tex]

Remember that

[tex](4a) ^ 2 = 4 ^ 2a ^ 2[/tex]

[tex]4^2a^2 -1=(4a)^2 -1[/tex]

As [tex]1 ^ 2 = 1[/tex] then

[tex](4a)^2 -1= (4a)^2 -1^2[/tex]

Remember that [tex]c ^ 2 -b ^ 2 = (c + b) (c-b)[/tex]

In this case [tex]c = 4a[/tex] and [tex]b = 1[/tex]

Finally

[tex](4a)^2 -1^2 = (4a-1)(4a+1)[/tex]

See attached picture for the answers.

Answer:

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer:

30% is greater than 0.03

Step-by-step explanation:

30% = 0.3, which is greater than 0.03

Answer:

Step-by-step explanation:

The formula of an area of a square with side z:

A = z²

We have z = 3/2. Substitute:

A = (3/2)² = (3/2)(3/2) = 9/4

Answer:

11x-6y

Step-by-step explanation:

we ignore the parenthesis so we add 8x and 3x since they are both positive which adds up to 11x

for -2y and -4y we add, a negative and a negative equals negative therefor -2y+(-4y)= -6y

11x-6y

For this case we must add the following expressions:

[tex](8x-2y) + (3x-4y) =[/tex]

We eliminate the parentheses, taking into account that:[tex]+ * + = +\\+ * - = -\\8x-2y + 3x-4y =[/tex]

We add similar terms:

[tex]8x + 3x-2y-4y =[/tex]

Equal signs are added and the same sign is placed:

[tex]11x-6y[/tex]

Answer:

[tex]11x-6y[/tex]

Option C

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope m = 71 and the point (-2, 4).

Substitute:

[tex]y-4=71(x-(-2))\\\\\bold{y-4=71(x+2)}[/tex]

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

Convert:

[tex]y-4=71(x+2)[/tex]         use the distributive property

[tex]y-4=71x+142[/tex]         add 4 to both sides

[tex]\bold{y=71x+146}[/tex]

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

Convert:

[tex]y=71x+146[/tex]            subtract 71x from both sides

[tex]-71x+y=146[/tex]        change the signs

[tex]\bold{71x-y=-146}[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

[tex]71x-y=-146[/tex]           add 146 to both sides

[tex]\bold{71x-y+146=0}[/tex]