Can you help me please.

Answer:

7 and 42

Step-by-step explanation:

The difference 35 is actually equivalent to 5 units if you draw it out into a model, thus 35 divide 5 is 7 and the other number is 7x6 which is 42

Answer:

Step-by-step explanation:

The given trigonometric expression is :

11 cos^2 x +3 sin^2 x+6sinx cosx +5

or, we can write it as,

(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5

Again, after rearranging the terms, we can write the whole expression as,

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

Then if you factor the following underlined section as you would with a polynomial:

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

You get:

(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5

Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.

So, now the whole expression becomes,

(3 cos x + sin x)^2 +7

Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),

The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.

So, I've attached a screenshot from a relevant document below:

Here, a=3 and b=1,

So, R= √10

As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.

Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.

i.e., in our case between (-√10) to √10.

Again, coming back to our original expression,

(3 cos x + sin x)^2 +7

The value of the term in bracket will lie between (-√10) and √10.

But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.

So, the minimum value will be,

(0)^2 + 7=7

and the maximum value will be,

(√10)^2 +7 = 17

Answer:

x = 1

Step-by-step explanation:

x² = x

x² / x = 1

x = 1

Check:

1² = 1

Answer:

An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.

Step-by-step explanation:

i didnt see a figure above but this is the answer to "what is the measure if obtuse angle in degrees?"

Answer: no real solutions

Step-by-step explanation:

8n^2-7n+7=0

a=8, b=-7, c=7

b^2-4ac=(-7)^2-4*8*7=49-224=-175

-175<0

no real solutions

Answer:

Substitute 6 for the variable, n, using parentheses. Then simplify by multiplying 8 and 6. 8(6) = 48. So you have 56 = 48, which is not a true statement. 6 is not a solution to the equation.

Step-by-step explanation:

hope it helps

Answer:

6

Step-by-step explanation:

5

Answer:

k = 10

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

2x(2x + kx) = 3x(3x + 5x)

4x² + 2kx² = 3x × 8x = 24x² ( subtract 4x² from both sides )

2kx² = 20x² ( divide both sides by 2x² )

k = 10

Answer:

Step-by-step explanation:

To evaluate the expression substitute the values of a , b , c and d into the above expression

a = - 9

b = - 7

c = 9

d = 3

So we have

2cd + 3ab = 2(9)(3) + 3(-9)(-7)

= 2(27) + 3( 63)

= 54 + 189

We have the final answer as

Hope this helps you

Answer:

Option (3)

Step-by-step explanation:

This question is not complete; here is the complete question.

Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?

Coordinates of the vertices of the triangle ABC are,

A(-3, 3), B(1, -3) and C(-3, -3)

When triangle ABC is reflected over y = -3

Coordinates of the image triangle A'B'C' will be.

A(-3, 3) → A'(-3, -9)

B(1, -3) → B'(1, -3)

C(-3, -3) → C'(-3, -3)

Further ΔA'B'C' is dilated by a scale factor of 2 about the origin then the new vertices of image triangle A"B"C" will be,

Rule for the dilation will be,

(x, y) → (kx, ky) [where 'k' is the scale factor]

A'(-3, -9) → A"(-6, -18)

B'(1, -3) → B"(2, -6)

C'(-3, -3) → C"(-6, -6)

Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

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

                      = [tex]\sqrt{52}[/tex]

                      = [tex]2\sqrt{13}[/tex]

Length of A"B" = [tex]\sqrt{(-6-2)^2+(-18+6)^2}[/tex]

                         = [tex]\sqrt{64+144}[/tex]

                         = [tex]\sqrt{208}[/tex]

                         = [tex]4\sqrt{13}[/tex]

Therefore, [tex]\frac{\text{AB}}{\text{A"B"}}=\frac{2\sqrt{13}}{4\sqrt{13}}[/tex]

[tex]\frac{\text{AB}}{\text{A"B"}}=\frac{\sqrt{13}}{2\sqrt{13}}[/tex]

[tex]AB(2\sqrt{13})=A"B"(\sqrt{13})[/tex]

Option (3) is the answer.

Answer:

I think that the answer is 1 to1

One shaded triangle has a base of 4.5 ft and a height of 9 ft, so its area is 0.5 * 4.5 * 9 = 20.25.

There are two such triangles, so the area of the shaded region is 40.5.

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

Answer:The integer represented by H is -2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Substitute the given numbers for the variables.

-(-2)(6-3)2

2(3)2

12

Answer:

1. Apples, Cauliflower, Green beans

2. Apples, Cauliflower, Salmon

...

27. Grapes, Corn, Almonds

Step-by-step explanation:

There are 3x3x3 = 27 combinations possible. You can enumerate them systematically.

Answer:

There are 27 combinations possible.

Hope this helps!

Answer:

92 is the smaller even integer

Step-by-step explanation:

x = first even integer

x+2 = second even integer

(x) + (x+2) = 186

Combine like terms

2x+2 = 186

Subtract 2 from each side

2x+2-2 =186-2

2x = 184

Divide by 2

2x/2 = 184/2

x = 92

x+2 = 94

Step-by-step explanation:

let,two even consecutive number be x and x+2

now,according to the question

x+x+2=186

or, 2x=186-2

or, 2x= 184

or, x= 184/2

:- x= 92

Hence,

x=92 and x+2= 94

two even consecutive numbers are 92 and 94

Answer:

17.50

Step-by-step explanation:

First find the discount

25 * .3

7.5

Subtract this from the original price

25-7.5

17.50

Answer:

[tex]SU=18[/tex]

Step-by-step explanation:

The segments ST and TU make up the line segment SU. Add the values to find SU:

[tex]ST+TU=SU\\\\13+5=18[/tex]

The length of SU is 18.

The length of SU is 18 units.

We have a point T is between S and U.

We have to determine the length SU.

According to the question -

ST = 13 units

TU = 5 units

Now -

SU = ST + TU = 13 + 5 = 18 units

Hence, the length of SU is 18 units.

To solve more questions on Line Segments, visit the link below-

brainly.com/question/19569734

#SPJ2

Answer:

40 degrees.

Step-by-step explanation:

Rotations are a rigid transformation and therefore preserve size and angles.

Answer:

Step-by-step explanation: 10 meters/3 meters =x/4.5 meters

Where x = the maximum distance the projector can be placed that can produce an image 4.5 meters high

3x = 10 (4.5)

3x = 45

X= 45/3

X= 15 meters

So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.

Answer:

Step-by-step explanation:

let the cost based on number of book bought be x and the constant be c:

4800 = 20x + c

8000 = 40x + c

c is common in both equations:

c =4800-20x

c = 8000-40x

equate the two:

4800-20x = 8000 - 40x

20x = 3200

x = 160

and c = 4800-20*160

c = 1600

Cost of 1000 books:

160*1000 + 1600

= 161600

Answer:

Area: x^2+x-6

Perimeter: 4x+2

Step-by-step explanation:

Area: multiply x+3 and x-2 and combine the like terms

Perimeter: multiply the length and width by two, then combine the like terms.

Answer:

Option A) A = 100(1.005)^12t

Step-by-step explanation:

The formula for Total Amount obtained using compound interest is given as:

A = P( 1 + r/n) ^nt

Where

A = Total amount received or obtained after investing

P = Principal or Initial Amount invested

r = interest rate

n = rate or number of times the interest is compounded

t = time in years.

In the question we obtained this values

P = $100

r = 6% = 0.06

n = compounded monthly, we have 12 months in a year, hence, n = 12

t = t

Using the compound interest formula for Amount A,

A = P( 1 + r/n) ^nt

A = 100(1 + 0.06/12)^12 × t

A = 100(1 + 0.005)^12t

A = 100(1.005)^12t

Therefore, the value of Mari's Investment if the interest is compounded monthly is

A = 100(1.005)^12t

Hence, Option A is correct.

Answer:

x = -1

Step-by-step explanation:

14x + 2 = 9x -3

Transpose

14x -9x = -3 -2

5x = -5

x= -5/5

x = -1

Answer:

x = -1

Step-by-step explanation:

[tex]14x+2=9x-3\\\\5x+2=-3\\\\5x=-5\\\\x=-1[/tex]

Answer:

x = 60

Step-by-step explanation:

Given

[tex]\sqrt{x+4}[/tex] - 7 = 1 ( add 7 to both sides )

[tex]\sqrt{x+4}[/tex] = 8 ( square both sides )

([tex]\sqrt{x+4}[/tex] )² = 8² , that is

x + 4 = 64 ( subtract 4 from both sides )

x = 60

Answer:

80 grades is the answer.

Step-by-step explanation:

72° into grades

1° = 10/9 grades

72° = 10/9 × 72grades

= 720/9 grades

= 80 grades

Answer:

80 grades

Step-by-step explanation:

72° into grades  

=>1° = 10/9 grades

=>72° = 10/9 × 72 grades  

=>72° = 720/9 grades

=>72° = 80 grades

Answer:

cos theta = √8/3

tan theta = √8/8

Step-by-step explanation:

sin theta = 1/3

1² + x² = 3²

x = √8

cos theta = √8/3

tan theta = 1/√8 = √8/8

Answer:

Option C. 2296 units² is the answer

Answer:

Option C, 2296 units²

Step-by-step explanation:

surfaceaArea of a rectangular prism,

2(wl+hl+hw)

= 2×(10×16+38×16+38×10)

= 2296 units²

Answer: D) w = 9 feet

Work Shown:

[tex]L = \sqrt{w^2+h^2}\\\\L^2 = w^2+h^2\\\\L^2-h^2 = w^2\\\\w^2 = L^2-h^2\\\\w = \sqrt{L^2-h^2}\\\\w = \sqrt{15^2-12^2}\\\\w = \sqrt{225-144}\\\\w = \sqrt{81}\\\\w = 9\\\\[/tex]

That points us to the final answer choice D.

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.

The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:

[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]

Combine like terms so we can get a simpler equation:

[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]

Now let's solve for x!

[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]

So [tex]x = 15[/tex].

Hope this helped!

Answer:

15

Step-by-step explanation:

3x + 6x + 45 = 180

9x = 135

x = 15

Answer:

The rule of the transformation is 6 units up and 3 units to the right [tex]T_{(3, \ 6)}[/tex] and an horizontal dilation of 2 as well as a vertical dilation of 4.

Step-by-step explanation:

The given coordinates of EFG and E'F'G' from the chart are;

E(3, 2)

F(9, 5)

G(9, 2)

E'(6, 8)

F'(18, 20)

G'(18, 8)

Therefore, we have, given that the y-coordinates of E and G are the same, the length of segment EG = 9 - 3 = 6 units

Similarly, given that the x-coordinates of F and G are the same, the length of segment FG = 5 - 2 = 3 units

The length of segment FE =  [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex] which gives;

Length from E(3, 2) to F(9, 5) = [tex]l = \sqrt{\left (5-2 \right )^{2}+\left (9-3 \right )^{2}} = 3 \cdot \sqrt{5}[/tex]

For similarly oriented E'F'G', we have;

E'G' = 18 - 6 = 12

F'G' = 20 - 8 = 12

E'F' = 12·√2

Therefore, the transformation is 6 units up and 3 units to the right and an horizontal dilation of 2 as well as a vertical dilation of 4.

The domain is the set of x values that has a corresponding y-values in a function or a graph.

The domain of the graph is: [tex]-10 \le x \le 10[/tex]

From the graph (see attachment), we have the following observation

These values can be represented as:

[tex]x_1= -10[/tex]

[tex]x_2 = 10[/tex]

So, the domain of x is: [tex]-10 \le x \le 10[/tex]

Read more about domain at:

https://brainly.com/question/24302079