Which expression is equivalent to (3b + 2r)+(4b + r)

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

B

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

2

4x² + 64 ← factor out the common factor of 4 from each term

= 4(x² + 16)

3

(a - 10)² = 121 ( take square root of both sides )

a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )

a = 10 ± 11

then

a = 10 - 11 = - 1

a = 10 + 11 = 21

Answer:

Step-by-step explanation:

A

Answer:

5ab

Step-by-step explanation:

8-3=5 just like 8ab-3ab=5ab

Answer:

D = 5

Step-by-step explanation:

1 plus 3 equals 4 plus 5 equals 9

Using the power reducing formulas the expression \(5cos^4(x) = 5(1 + cos(2x))^{2/4}\).

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

\(cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2\)

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

\(cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)\)

Now we have:

\(cos^2(x) = (1 + cos(2x))/2\)

Thus,

\(cos^4(x) = (1 + cos(2x))/2)^2\)

Now multiplying by 5:

\(5cos^4(x) = 5(1 + cos(2x))^{2/4}\)

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Answer:

Yes

Step-by-step explanation:

a+bx is the formula so the slope is negative 8 and the y intercept is -21.

Answer:

Complementary angles

Step-by-step explanation:

When two angles add up to 90°, they are Complementary to each other.

Here, ∠DAB = 90° (right angles)

It means, ∠DAB = ∠BAE (vertically opposite angles)

Also, ∠BAE = a + b

So, a+b is equal to 90°. Hence, the correct option is (b) "Complementary angles".

Answer:

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

400*.25=100

400-100=300

Hope this helps!!

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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None of the solutions are appropriate since the result of the equation z + (z+6) will be equal to 2z + 6.

A mathematical expression is the result of combining a number of mathematical symbols with an arithmetic operator, a variable, and a constraint.

In a different sense, expression is highly helpful in identifying the root or end value of a constraint.

for instance, 3x + 5y

The expression restriction is denoted by the symbols = or, >.

Given the phrase,

z + (z+6)

opening the bracket

z + z + 6

⇒ 2z + 6

Hence

"2z + 6 will be the value of the equation z + (z+6)."

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Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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the measure of Angle D in the given triangle is 45 degrees, which is option B.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's faces, that converge upon the vertex, and center, within its shape. A surface angle may be created by the configuration of two rays. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible shape for two lines or rays without a common termination in planar geometry. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of both of the rays' common endpoints is called the vertex, which is sometimes referred to as either side of an angle.

given,

In a triangle, the sum of the angles is always 180 degrees. Therefore, to find the measure of angle D in the given triangle, we can use the fact that:

Angle A + Angle B + Angle D = 180 degrees

We are given that Angle A is 45 degrees. We can see from the diagram that Angle B is a right angle, which means it measures 90 degrees. As a result, we may enter the following numbers into the formula above to obtain:

45 + 90 + Angle D = 180

Simplifying the equation, we get:

135 + Angle D = 180

Subtracting 135 from both sides, we get:

Angle D = 45 degrees

Therefore, the measure of Angle D in the given triangle is 45 degrees, which is option B.

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Answer:

1. D

2. Is A $0.87 for each song

Step-by-step explanation:

12 x $0.87 = $10.44

$10.44 + $5.04 = $15.48

I hope this helped you

Note: Here tax rate is note given. Consider the tax is not applied.

Given:

Lin’s Father is paying for $50 meal.

Discount = 15%

To find:

The price of a discounted meal before the tax.

Solution:

Let x be the price of a discounted meal before the tax.

According to the question,

Price of meal after discount = Price of meal before discount - Discount

\(50=x-\dfrac{15}{100}\times x\)

\(50=x-0.15x\)

\(50=0.85x\)

Divide both sides by 0.85.

\(\dfrac{50}{0.85}=x\)

\(58.823529=x\)

\(x\approx 58.824\)

Therefore, the price of a discounted meal before the tax is $58.824.

Answer:

3

Step-by-step explanation:

(x + 1) : (3x + 1) = 8 : 20

20(x + 1) = 8(3x + 1)

20x + 20 = 24x + 8

12 = 4x

x = 3

Answer:

0

Step-by-step explanation:

The scale of the number line is by 2's. You can determine this because the number between -10 and -6 is -8. SO if you continue this pattern of increasing the number by 2, you get -6, -4, -2, then 0.

Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.

The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.

1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.

A

1   4

2   8

3   9

4   5

5   2

6   7

7   7

8   5

9   8

2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.

3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.

4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.

5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.

Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.

In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.

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Answer:100

Step-by-step explanation:

40+40 =80 +20=100

Answer: 1

Step-by-step explanation:

take two points from the line, like (3,0) & (0,-3)

now slope = (-3-0)/(0-3) = 1

Answer:

5/9 = 25/45

Step-by-step explanation

multiply 5/9 by 5/5 this will turn it into 25/45

5x5=25

5x9=45

Answer:

16 teachers.

Step-by-step explanation:

84 / 21 = 4

4 * 4 = 16

Hope this helped. Please give brainly if its the best!

Answer:

\( \huge \colorbox{blue}{16 students}\)

Step-by-step explanation:

we are given the ratio of students and teachers:

\( \displaystyle \: \frac{21}{4} \)

which means if the number of students is 21 then the number of teachers should be 4

to find how many teachers should go if students 84 we have to divide 84 by \(21/4\) :

\( \displaystyle \: 84 \div \frac{21}{4} \)

simplify division:

\( = \displaystyle \: 84 \times \frac{4}{21} \)

simplify multiplication:

\( = \displaystyle \: \cancel{ 84} \: ^{4} \times \frac{4}{ \cancel{21}} \\ = 4 \times 4 \\ = 16 \)

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

I think the answer you're looking for is -49.05

(longer version: -49.0504)

a.

The rebate is:

Therefore, the rebate is $710

b.

To determine the percent of the rebate we use a rule of three:

then:

Therefore the rebate is 4.17%

c.

The amount of the cash discount is:

Therefore, the amount of the cash discount is $163.35

d.

The dealers final price is:

Therefore, the dealer's final price is $16171.65

e.

The dealer's total savings is:

Hence the dealer's total savings is $873.35