Evaluate the expression
8
-
d
+3 when d = 4

Given that ∠ADB and ∠CDB are complimentary angles, the numerical measure of angle CDB is 25 degrees.

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

Given that;

Since ∠CDA is a right triangle, the sum of ∠ADB and ∠CDB sums up to 90 degrees.

∠ADB + ∠CDB = 90°

(7x +2) + (3x - 2) = 90

Solve for x

7x +2 + 3x - 2 = 90

7x + 3x - 2 +2 = 90

10x = 90

x = 90/10

x = 9

Now, the numerical measure of angle CDB will be;

m∠CDB = (3x - 2)

Plug in x=9

m∠CDB = 3(9) - 2

m∠CDB = 27 - 2

m∠CDB = 25 degrees

Given that ∠ADB and ∠CDB are complimentary angles, the numerical measure of angle CDB is 25 degrees.

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Answer:

6²

Step-by-step explanation:

6² is 6×6 which is 36

if you write it as 6² then:

6²=6^x

since the bases are equal you can cancel out the bases and it becomes:

x=2

Answer:

a. 6^2

Step-by-step explanation:

A because six times itself is equal to 36.

here you go :) explanation up top

Can someone help explain how to solve

In the picture there are 4 question that are

1) [tex]A(-6,-2)\rightarrow A^{'}(-6,2)\\B(-3,-6)\rightarrow B^{'}(-3,6)\\C(-2,-2)\rightarrow C^{'}(-2,2)\\[/tex]

2)[tex]D(15,10)\rightarrow D^{'}(6,4)\\E(5,10)\rightarrow E^{'}(2,4)\\F(10,-5)\rightarrow F^{'}(4,-2)\\[/tex]

3)[tex]G(-2,7)\rightarrow G^{'}(-7,-2)\\H(-4,8)\rightarrow H^{'}(-8,-4)\\I(-3,5)\rightarrow I^{'}(-5,-3)\\[/tex]

4) [tex]J(11,-8)\rightarrow J^{'}(1,-5)\\K(6,-1)\rightarrow K^{'}(-4,2)\\L(3,-7)\rightarrow L^{'}(-7,4)\\[/tex]

The transformation has the following form:

1)[tex](x,y)\rightarrow(x,-y)[/tex]

2)[tex](x,y)\rightarrow\frac{2}{5}(x,y)[/tex]

3)[tex](x,y)\rightarrow(-y,x)\\[/tex]

4) It does not have transformation.

Geometric Transformation:

Images of triangles, quadrilaterals, pentagons, and other geometric shapes can undergo geometric transformations through the vertices in a Cartesian plane. Reflection, rotation, and translation are the three transformations; they only affect the geometric figure's location and not its size. Expansion and contraction are the two transformations that alter the geometric figure's size.

It is necessary to know the sort of transformation that took place given the points and their transformations.

1) We observe that point transformation A,B and C are transformed.

The transformation has the following form:

[tex](x,y)\rightarrow(x,-y)[/tex]

Every x-value remains constant, while every y-value flips from what it was.[tex](x,y)\rightarrow(x,-y)[/tex]

2)We observe that point transformations D, E, and F are contractions. Let's now identify the scalar that was applied to the transformation. We compute the product of the original point's coordinate and one of the transformation point's coordinates.

[tex]\frac{D^{'} _{y} }{D_{ y}} =\frac{4}{10} =\frac{2}{5}[/tex]

We multiply the coordinates of points E and F and check the results to make sure this is true.

For E:

[tex]\frac{2}{5} (5,10)=(2,4)\\Therefore,E^{'} =(2,4)[/tex]

For F:

[tex]\frac{2}{5} (10,-6)=(4,-2)\\Therefore,F^{'} =(4,-2)[/tex]

Therefore, The transformation has the following form:

[tex](x,y)\rightarrow\frac{2}{5}(x,y)[/tex]

3)We observe that point transformation G,H and I are transformed.

The transformation has the following form:

[tex](x,y)\rightarrow(-y,x)[/tex]

Every y-value flips from what it was to the opposite. The x and y values are reversed.[tex](x,y)\rightarrow(-y,x)[/tex]

4)We observe that point transformation J,K and L are not transformed.

It does not satisfy the condition of the transformation.

Therefore, this is how we solve the transformation.

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Answer: X=365/83 OR x= 4.39

Step-by-step explanation:

One year from now, there are 300 freshmen, 1425 sophomores, 1375 students that transferred out, and 3900 students graduated.

Each category is based on the percentages given, 25% of students transfer, 15% have to repeat the year, and 60% complete the year and the fact that once a student has transferred or graduated they have a 100% chance of staying classified that way.

Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".

If currently there are 2,000 freshmen, 1,500 sophomores, 500 students that have transferred, and 3,000 graduates,

Among the 2000 freshmen, 25% of students transfer, 15% have to repeat the year, and 60% complete the year.

students who transfer = 25% of 2000 = 500

freshmen(repeater) = 15% of 2000 = 300

sophomore = 60% of 2000 = 1200

Among the 1,500 sophomores, 25% of students transfer, 15% have to repeat the year, and 60% complete the year.

students who transfer = 25% of 1500 = 375

sophomore(repeater) = 15% of 1500 = 225

students who graduated = 60% of 1500 = 900

Adding the total number of sophomores(freshmen who completed the year and sophomores that have to repeat the year)

sophomores = 1200 + 225 = 1425

Adding the total number of students who transfer,

500 + 500 + 375 = 1375

Adding the total number of student that graduated,

3000 + 900 = 3900

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The transformation used to map AB to A'B' is not a rigid transformation since the measure of AB is greater than the measure of A'B' and not equal.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

A rigid transformation is a transformation that preserves the shape and size such as rotation, reflection and translation.

Given the points A(-1, 13), B(1, 5), A'(2, 3), and B'(6, 1), hence:

[tex]AB=\sqrt{(5-13)^2+(1-(-1))^2} =\sqrt{68}\\\\A'B'=\sqrt{(1-3)^2+(6-2)^2}=\sqrt{20}[/tex]

The transformation used to map AB to A'B' is not a rigid transformation since the measure of AB is greater than the measure of A'B' and not equal.

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Answer:

140 miles

Step-by-step explanation:

Let's solve the equation step by step,

Step 1: Substract the daily charge of $25 from $39

➟ $39 - $25

➟ $14 {remaining cost except daily rate}

Step 2: Divide $14 by cost per mile

➟ $14/0.10

➟ 140 {total mile driven}

∴ He/she drove 140 miles

Answer: 140 Miles

Step-by-step explanation:

39-25= 14

14/.10 = 140

Answer:

Step-by-step explanation:

Here ya go!

The current location of G is (-4,3)

If it was translated to the left by four units, that would be an extra -4

so our new coordinates are (-8,3)

Now if we translate it up 3 units, thats adding 3

so our new coordinates are

(-8,6)

Hope this helps!^^

The equation of line for m = 5/6 and the y -intercept is (0,12) is y = 5/6x + 12.

The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

The equation for line is y = mx + c

Given, m = 5/6, y-intercept = (0,12)

now putting the values in the equation,

y = 5/6x + 12

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The two angles are 45° and 135°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

One of the same side angles of two parallel lines is three times the other angle.

According to given question we have

Let the smaller side= x,

The larger side = 3x.

The two angles are supplementary.

x + 3x = 180°

4x = 180°

Divide by 4 on both sides we get,

x = 45°

3x = 135°

Therefore,  the two angles are 45° and 135°.

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By combining the like terms, the simpler form of expression -(8a+3b)+10(2a-5b)  is 12a-53b

Given,

The expression = -(8a+3b)+10(2a-5b)

Expand the terms

-(8a+3b)+10(2a-5b)= -8a-3b+20a-50b

Combining like terms

-8a-3b+20a-50b = 12a-53b

Hence, by combining the like terms, the simpler form of expression is -(8a+3b)+10(2a-5b) 12a-53b

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Answer:

English: 48 minutes

Math: 54 minutes

Biology: 18 minutes

Step-by-step explanation:

Set up each subject with the variable x as the biology homework.:

English: (x+30)

Math: (3x)

Biology: (x)

Now add them together and set it equal to 120 (2 hours into minutes):

x + 30 + 3x + x = 120

Move 120 over to the left and simplify:

5x - 90 = 0

Solve:

5(x - 18) = 0

x - 18 = 0

x = 18

So biology is 18 minutes, and then plug 18 in for all the other subjects:

English: 18+30=48 minutes

Math: 3*18=54 minutes

Biology: 18 minutes

Answer: 203.057

Step-by-step explanation:

75.2+123.96+3.897

199.16+3.897

203.057

Answer:

It the square with 3/4 shaded. the point shows 0.75 and the square shows 75% which is 3/4.

The solution of the given linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is at w = 3.

According to the given question.

We have a linear equation in one variable.

12 -3(2w + 1) = 7w -3(7 + w)

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is given by

12 - 3(2w + 1) = 7w - 3(7 + w)

⇒ 12 - 6w -3 = 7w - 21 -3w                 (by distributive rule)

⇒ 9 - 6w = 4w - 21                          (subtracting the like terms)

⇒ 9 + 21 = 4w + 6w

⇒ 30 = 10w

⇒ 30/10 = w

⇒ w = 3

Hence, the solution of the given linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is at w = 3.

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Answer:

49 cards in each binder

Step-by-step explanation:

If there are 5 binders and each binder contains the same amount of cards, you can just do 245 divided by 5 which gives you 49.

Answer:

(6x² - 5)(x² + 2)

Step-by-step explanation:

6x⁴ - 5x² + 12x² - 10

(6x⁴ - 5x²)  (12x² - 10)

x²(6x² - 5) + 2(6x² - 5)

(6x² - 5)(x² + 2)

I hope this helps!

Answer:

Step-by-step explanation:

So we have 6x4-5x2+12x2-10

So we are going to add same elements

-5x2+12x2=7x2

so now we have

6x4 +7x2-10

Let u=x2

6u2+7u-10

Now we factor

(6u-5)(u+2)

Replace x2 for u

(6x2-5)(x2+2)

Hope this helps!^^

Answer: SA=326.56 inches

Step-by-step explanation:

[tex]SA=2\pi r^2+2\pi rh\\SA=2\pi r(r+h)\\r=4 \ inches\ \ \ \ \ h=9\ inches\ \ \ \ \ \ \pi =3.14\\Hence,\\SA=(2)(3.14)(4)(4+9)\\SA=(25.12)(13)\\SA=326.56\ inches[/tex]

$2950 is the monthly salary of the other employee.

a. the given information = mean of two salaries =  3210

                                        = salary of 1st employee =3470

the unknown information = salary of 2nd employee = 2950

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

We know that mean, [tex]m = \frac{\text{sum of the terms}}{\text{number of terms}}[/tex]

Here is given the

mean = 3210

term₁ = 3470                 (salary of one of the employees)

term₂ = ?                          (salary of the 2nd employee)

So, if we simplify

⇒ [tex]m = \frac{\text{sum of the terms}}{\text{number of terms}}[/tex]

⇒ [tex]3210 = \frac{3470 + term_2}{2}[/tex]

⇒ [tex]3210[/tex] × [tex]2 = 3470 + term_2[/tex]

⇒ [tex]6420[/tex] = [tex]3470 + term_2[/tex]

⇒ [tex]term_2 = 6420 - 3470[/tex]

⇒ [tex]term_2 = 2950[/tex]

So, the salary of the other employs is $ 2950

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The distance of AO and BO are the same so the given triangle will be an isosceles triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

The given vertices are making a triangle as shown below in the figure.

Distance between A(5,12) and O(0,0) is

⇒ [tex]\sqrt{(5 - 0)^2 + (12 - 0)^2}[/tex]

⇒ 13

Distance between B(13,0) and O(0,0) is

⇒ [tex]\sqrt{(13 - 0)^2}[/tex]

⇒ 13

Since the two sides are the same so triangle will be isosceles.

Hence "The distance of AO and BO are the same so the given triangle will be an isosceles triangle".

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Using Venn sets, it is found that:

For this problem, we consider the following sets:

2 are taking all subjects, hence:

(A ∩ B ∩ C) = 2.

8 are taking chemistry and math, hence:

(A ∩ C) + (A ∩ B ∩ C) = 8.

(A ∩ C) = 6.

6 are taking math and english, hence:

(A ∩ B) + (A ∩ B ∩ C) = 6.

(A ∩ B) = 4.

4 are taking chemistry and english, hence:

(B ∩ C) + (A ∩ B ∩ C) = 4.

(B ∩ C) = 2.

15 are taking chemistry, hence:

C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 15.

C + 6 + 2 + 2 = 15.

C = 5.

20 are taking english, hence:

B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 20

B + 4 + 2 + 2 = 20

B = 12.

18 are taking math, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 18

A + 4 + 6 + 2 = 18

A = 6.

There is a total of 40 students, hence:

None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 40.

None + 6 + 12 + 5 + 4 + 6 + 2 + 2 = 40.

None + 37 = 40.

None = 3.

Hence:

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Answer:

6^5 is equals to 7776 and 7776×6^-5 is equals to 1

The equation of the line in slope-intercept form with a slope of 1/2 and y-intercept of (0 , 0) is y = 1/2 x.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given that the slope of the line is 1/2 and the y-intercept is (0 , 0), write the equation of the line by simply plugging in its values.

y = mx + b

y = (1/2)x + 0

y = 1/2 x

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Answer:

s = 8 cm

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 64 cm² , then

s² = 64 ( take square root of both sides )

s = [tex]\sqrt{64}[/tex]

s = 8 cm

to get the equation of any straight line, we simply need two points off of it, again, let's use the ones from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{11}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{11}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 4 }{ 2 }\implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{2}(x-\stackrel{x_1}{2}) \\\\\\ y-7=2x-4\implies {\LARGE \begin{array}{llll} y=2x+3 \end{array}}[/tex]

The correct answers would be options (A) and (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given two cases,

p: -3x + 8x - 5x = x

q: (3x)(5y) = 15xy

We have to need to isolate the variables:

p: -3x + 8x - 5x = x

⇒  (-3x - 5x) + 8x = x

⇒  -8x + 8x = x

⇒ x = 0

This is not always true, hence the statement is incorrect because this will hold true for only one value of x.

q: (3x)(5y) = 15xy

⇒ (3x)(5y) = 15xy

⇒ (3×5)(x×y) = 15xy

⇒ 15xy = 15xy

If both x and y are true for any value, then the statement is true.

Hence, p → q and q → p are false.

Therefore, the correct answers would be options (A) and (C).

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Answer:

x=6.24

Step-by-step explanation:

cos 78° =adj/hyp=x/30

cos 78° =x/30

x=cos 78°×30

x=0.2079×30

x=6.237350725

to the nearest hundredth

x=6.24

Step-by-step explanation:

Question no 23 : Option d

Question no 21:

angles on a straight lin is equal to 180°

150-180 = 30 (option d)

I just answered question no 23 and 21

re check the answers if you can I am a student too just trying to help as much as I can.