The sum of two angles measures is 95 degrees. Angle 2 is 40 degrees smaller than 2 times angle 1. What are the measures of the two angles in degrees?

ANSWER:

7x + 3

let us break the problem into two smaller equations that match-

5x + 2x = 7x

9 - 6 = 3

this leaves you with 7x + 3.

Answer:

Vertical Distance = [tex]y_{2}-y_{1}[/tex]

Step-by-step explanation:

Here we are asked about the formula for vertical distance between two coordinates.

Suppose there are two coordinates

[tex](x_{1},y_{1})  ; (x_{2},y_{2})[/tex]

Vertical distance between two coordinates is the distance between the y coordinates of the two coordinates.

This can be find out with the formula

[tex]D_{y}=y_{2}-y_{1}[/tex]

For example:

Let two coordinates are (2,4) and (5,2)

Here the vertical distance can be find by using above formula as

[tex]D_{y}[/tex]=4-2

[tex]D_{y}[/tex]=2 units.

Answer:

<2 = 97

Step-by-step explanation:

Definition: Supplementary angles are 2 or more angles with the same vertex that add up to 180o

Solution

<1 = 83

<2 = ?

Total = 180o

<1 + <2 = 180                   Substitute for angle 1

83 + <2 = 180                  Subtract 83 from both sides.

83 - 83 + <2 = 180 - 83   Do the subtraction

<2 = 97 degrees

The supplement of an 83-degree angle is the angle that adds up to 180 degrees with it. By subtracting 83 from 180, we find that the supplement of the angle is 97 degrees.

The question is asking for the supplement of an angle that measures 83 degrees. In geometry, the supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. To find the supplement of an 83-degree angle, you subtract 83 from 180.

Step-by-step solution:

Answer: The value of the y-intercept is [tex]-\frac{3}{5}[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

In this case we know that the line passes through point [tex](0.4,-\frac{1}{2})[/tex] and has a slope of [tex]\frac{1}{4}[/tex]. Then we can substitute the following values into  [tex]y=mx+b[/tex]:

[tex]x=0.4\\\\y=-\frac{1}{2}\\\\m=\frac{1}{4}[/tex]

Then:

[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b[/tex]

And finally, we must solve for "b":

[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b\\\\-\frac{1}{2}-\frac{1}{10}=b\\\\b=-\frac{3}{5}[/tex]

For this case we have that by definition, the slope-intersection equation of a line is given by:

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

Where:

m: It's the slope

y: It is the cut point with the "y" axis

They tell us as data that:

[tex]m = \frac {1} {4}[/tex]

So, the equation is:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute the given point to find "b":

[tex]- \frac {1} {2} = \frac {1} {4} (0.4) + b\\- \frac {1} {2} = \frac {0.4} {4} + b\\b = - \frac {1} {2} - \frac {0.4} {4}\\b = -0.5-0.1\\b = -0.6[/tex]

Thus, the cut point with the y axis is -0.6

Answer:

[tex]b = -0.6[/tex]

Using the Pythagorean theorem with the length of the ladder as the hypotenuse and the base distance as one side, we calculate the height of the building to be approximately 10.82 feet.

The student's question can be solved using the principles of the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario, the ladder, the building, and the ground form a right triangle.

The ladder serves as the hypotenuse, the height of the building is the opposite side, and the distance from the ladder's base to the building is the adjacent side.

To find the height of the building, we can set up the equation using the Pythagorean theorem as follows:

a2 + b2 = c2

where a is the distance from the base of the ladder to the building (2 feet), b is the height of the building, and c is the length of the ladder (11 feet).

Plugging in the values we have:

22 + b2 = 112,4 + b2 = 121,b2 = 121 - 4,b2 = 117.

Therefore, the height of the building is:

b = √117 ≈ 10.82 feet.

The building is approximately 10.82 feet tall.

Answer:

Sprite: 5/8

Step-by-step explanation:

Let's assume the amount poured out was equal of both liquids:

Convert them into eighths:

Fruit juice: 4/8

Sprite: 4/8

Now to remove 1/4 total we need to remove 1 of each:

Fruit juice: 3/8

Sprite: 3/8

Now add those two we took off to the Sprite:

Fruit juice: 3/8

Sprite: 5/8

[tex]\frac{7}{8}[/tex] of the punch is now Sprite

For given question,

Abby pours out  [tex]\frac{1}{4}[/tex]  of the liquid, and then fills the bowl up again with Sprite.

This means, the fraction of Sprite in the bowl is,

[tex]1-\frac{1}{4} = \frac{3}{4}[/tex]             ................(i)

We know that the liquid has  [tex]\frac{1}{2}[/tex] fruit juice and [tex]\frac{1}{2}[/tex] Sprite.

This means, out of [tex]\frac{1}{4}[/tex] of poured liquid [tex]\frac{1}{2}[/tex] is Sprite.

So, the amount of Sprite in the liquid would be,

[tex]\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}[/tex]                           ..................(ii)

Now we find the total fraction of Sprite in the punch.

From (i) and (ii),

[tex]\frac{3}{4}+\frac{1}{8}\\\\ =\frac{3\times 2}{4\times 2}+\frac{1}{8}\\\\ =\frac{6}{8}+\frac{1}{8}\\\\ =\frac{7}{8}[/tex]

Therefore, [tex]\frac{7}{8}[/tex] of the punch is now Sprite

Learn more about the fraction here:

brainly.com/question/12151403

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b*h/2 is the formula for area

8*h= 24

24*2= 48

48/8= 6

6 is the height/ missing side

The value of x for the given right angle triangle such that its area is 24 units² will be 8.

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.

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.

As per the given triangle,

The area of right angle triangle = (1/2)8 × x

(1/2)8 × x = 24

x = 24/4 = 8

Hence "The value of x for the given right angle triangle such that its area is 24 units² will be 8".

For more about triangles,

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Answer: Option A.

Step-by-step explanation:

The surface area of a right rectangular prism can be calculated with this formula:

[tex]SA = 2(wl + lh + hw)[/tex]

Where "w" is the width. "l" is the lenght and "h" is the height.

We know that:

[tex]w=6in\\l=9in\\h=18in[/tex]

Knowing this values, we can substitute them into the formula.

Therefore we get that the surface area of a right rectangular prism is this:

[tex]SA = 2[(6in)(9in) + (9in)(18in) +(18in)(6in)][/tex]

[tex]SA=648in^2[/tex]

This matches with the option A.

Answer:

0.76

Step-by-step explanation:

The mean of the data including the outlier is:

Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87 + 48.32 + 41.59 + 42.71)/12 = 39.98 seconds.

In this case, the outlier comes to be the data: 48.32. If we don't consider that data point, the mean equals:

Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87  + 41.59 + 42.71)/11 = 39.22

The difference is:  39.98 - 39.22 = 0.76

Answer:

C . 0.76

Step-by-step explanation:

We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:

Jan  40.55 Feb 41.51

March 42.01 Apr 38.76

May 36.32  June 34.28

July 35.38  Aug 37.48

Sept 40.87 Oct 48.32

Nov 41.59 Dec 42.71

We have to find the difference between the mean of the data , including the outlier and excluding the outlier

Outlier: That observation which is different from other observations.

The outlier in the given observations is 48.32 because is different from other observations.

Mean of the data including the outlier

Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]

Mean=[tex]\frac{479.78}{12}[/tex]

Mean=39.982

Mean of the data excluding the outlier

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}

Mean=[tex]\frac{431.46}{11}[/tex]

Mean=39.224

Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758

Difference between mean of the data including the outlier and excluding the outlier=0.76

Answer Answer:

Step-by-step explanation:

We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:

Jan  40.55 Feb 41.51

March 42.01 Apr 38.76

May 36.32  June 34.28

July 35.38  Aug 37.48

Sept 40.87 Oct 48.32

Nov 41.59 Dec 42.71

We have to find the difference between the mean of the data , including the outlier and excluding the outlier

Outlier: That observation which is different from other observations.

The outlier in the given observations is 48.32 because is different from other observations.

Mean of the data including the outlier

Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]

Mean=[tex]\frac{479.78}{12}[/tex]

Mean=39.982

Mean of the data excluding the outlier

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}

Mean=[tex]\frac{431.46}{11}[/tex]

Mean=39.224

Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758

Difference between mean of the data including the outlier and excluding the outlier=0.76

Answer :C . 0.76

The answer is b because the ratio is blondes to brunettes.

Follow below steps;

The student asked which statement about the proportions of blonds and brunettes among their 15 friends is false. Given that the proportion of blonds to brunettes is 6 to 9, let's evaluate the options:

Option a) The ratio of the number of friends to brunettes is 15 to 9. This statement is true since there are 15 friends in total and 9 of them are brunettes.

Option b) The ratio of brunettes to blonds is 6 to 9. This statement is false because the proportion of blonds to brunettes is 6 to 9, so the ratio of brunettes to blonds should be 9 to 6.

Option c) The ratio of blonds to the number of friends is 6 to 15. This statement is true because there are 6 blonds out of 15 friends.

Option d) The ratio of brunettes to the number of friends is 9:15. This statement is also true because there are 9 brunettes out of 15 friends.

Therefore, option b is the false statement as the ratio of brunettes to blonds is incorrectly stated as 6 to 9 instead of the correct ratio 9 to 6.

Check the picture below.  So the sector looks more  or less like that one.

we know a full circle has an arc of 2π, so how much is 7/8 of 2π?  well, is simply its product.

[tex]\bf ~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\pi \cdot \cfrac{7}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{7\pi }{4}[/tex]

Certainly! Let's find the measure of the sector's arc given the ratio of the sector's area to the total area of the circle.
First, let's denote the area of the circle as A and the area of the sector as S.
We are given that the ratio S/A = 7/8. The total area of a circle is given by the formula A = πr^2 (where r is the radius of the circle), but since we are dealing with ratios, we don't need the specific values for π or r, as they will cancel out.
Now, the area of a sector of a circle is a fraction of the total area of the circle. This fraction is equal to the angle θ (in degrees) of the sector divided by the total angle in the circle (which is 360 degrees). So, the area of the sector S can be calculated by the formula:
\[ S = \frac{θ}{360} \times A \]
Now let's use the given ratio:
\[ \frac{S}{A} = \frac{7}{8} \]
\[ \frac{\frac{θ}{360} \times A}{A} = \frac{7}{8} \]
\[ \frac{θ}{360} = \frac{7}{8} \]
Next, we cross-multiply to solve for θ:
\[ 8θ = 7 \times 360 \]
\[ θ = \frac{7 \times 360}{8} \]
\[ θ = 7 \times 45 \]
\[ θ = 315 \]
So, the measure of the sector's arc is 315 degrees.

Answer:

D

Step-by-step explanation:

Given

- 4(x - 6) + 3(a - 7)

distribute the first parenthesis by - 4 and the second by 3

= - 4x + 24 + 3a - 21

= - 4x + 3a + 3 → D

Answer:

The solution is -2/7 not –14.

Answer:

its D

Step-by-step explanation:

Answer:

the answer is 78

Step-by-step explanation:

subtracting 141 from both sides

[tex]y+141-141=219-141\\simplify\\y=78[/tex]

Answer:

The answer is 78.

Step-by-step explanation:

To find y or the answer, you must do the inverse operation when you want to the value of the unknown. So in this case, we must use subtraction. Also, in this process you must replace y with 219. After doing this, the equation will read [tex]219 - 141 = y.[/tex] Now isolate the equation.

Ex.

[tex]219 - 141 = 78.[/tex]

Therefore, the answer is 78.

P.S. That is the way how I can explain it to you. If you have any other requirements, please contact me (with my brainly account).

Answer:

[tex]x^{24}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]

Hence

[tex](x^{3}) ^{8}[/tex] = [tex]x^{3(8)}[/tex] = [tex]x^{24}[/tex]

Answer:

9 and -4

Step-by-step explanation:

Find two numbers that multiply to be -36 and add to be -5.

That is -9 and 4.

So the factored form of x^2-5x-36 is (x-9)(x+4)

So the x-intercepts are 9 and -4

Answer: The answer is below, so the picture shows  you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle. The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

* Which means this triangle is a 30° - 60° - 90°.

* Hopefully this helps:) Mark me the brainliest:)!!!!

This is a right triangle

Answer:

x<1.5

Step-by-step explanation:

The equation is

[tex]f(x)=-x^2+3x+8[/tex]

Use a graphing tool to find the vertex of the parabola.When you get the vertex from the graph, you can now write the increase as ; all x-values less than the x-value of the vertex value in the graph

From the graph, the vertex is at (1.5,10.25), the parabola opens down with maximum value y=10.25

The interval of increase is x<1.5

Answer:

[tex]x \geq \frac{3}{2}[/tex]

Step-by-step explanation:

First, the first derivative of the function is computed to distinguish which interval is increasing.

[tex]f'(x) = -2\cdot x + 3[/tex]

An interval is increasing only if slope is increasing as long as x increases. Then, it is quite evident that curve is increasing for:

[tex]x \geq \frac{3}{2}[/tex]

Answer:

Her mistake was that she should have used –1 for moving below the lobby.

Step-by-step explanation:

Lets denote the lobby as Floor zero (0)

- if you go up, you add a positive value to this quantity.

- if you go down, you add a negative value to this quantity.

Lets assume that moving through each floor is equivalent to advancing one unit

* She first took an elevator one floor down

(-1)

Then she took the elevator back up 5 floors to her office

(+5)

Her movement is described by the expression

(-1) + (5)

Her mistake was that she should have used –1 for moving below the lobby.

Answer:

A

Step-by-step explanation:

Answer:

x < 48.8 ≈ 49

Step-by-step explanation:

11.22x − 200 < 347.96

add 200 to both sides

11.22x − 200 + 200 < 347.96 + 200

11.22x < 547.96

divide via by 11.22

x < 547.96/11.22

x < 48.8 ≈ 49

Answer: The value of x < 48.83.

Step-by-step explanation:

Since we have given that

[tex]11.22x-200<347.96[/tex]

We need to find the value of x:

First we add 200 on the both sides:

[tex]11.22x-200+200<347.96+200\\\\11.22x<547.96[/tex]

Now, we divide it by 11.22 on both the sides:

[tex]\dfrac{11.22x}{11.22}<\dfrac{547.96}{11.22}\\\\x<48.83[/tex]

Hence, the value of x < 48.83.

Answer:

A

Step-by-step explanation:

Since we are given self defining variables, h is obviously referring to the plant's height and y is referring to the plant's years or age.

Then, since a plant's height is 1.4 times its age, age multiplied by 1.4 should be the plants height.

The equation would come out to [tex]h=1.4y[/tex]

[tex]\bf \stackrel{\textit{difference of squares}}{(6+3i)(6-3i)}\implies (6)^2-(3i)^2\implies \stackrel{\textit{recall }i^2=-1}{36-(3^2 i^2)}\implies 36-(9\cdot -1) \\\\\\ 36+9\implies 45[/tex]

Step-by-step explanation:

6*6 - 6*3i + 6*3i -3i*3i

36-18i+18i-9i^2

36-9(-1)= 36+9= 45

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

12/√7+2

Rationalize the denominator

=12/7+2 * √7-2/√7-2

=12√7-24/7-4

=12√7-24/3

By taking common from numerator we get

=12(√7-2)/3

=4√7-8

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

Answer:

Part 1) The vertex is the point (0.50,2.50)

part 2) [tex]y=-58[/tex]

Step-by-step explanation:

we have

[tex]y=-2x^{2} +2x+2[/tex]

Part 1) Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y-2=-2x^{2} +2x[/tex]

Factor the leading coefficient

[tex]y-2=-2(x^{2} -x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]y-2-0.50=-2(x^{2} -x+0.25)[/tex]

[tex]y-2.50=-2(x^{2} -x+0.25)[/tex]

[tex]y-2.50=-2(x-0.50)^{2}[/tex]

[tex]y=-2(x-0.50)^{2}+2.50[/tex] -----> equation in vertex form

The vertex is the point (0.50,2.50)

Part 2) Find the value of y for x=6

substitute the value of x in the equation

[tex]y=-2(6)^{2} +2(6)+2[/tex]

[tex]y=-72 +12+2[/tex]

[tex]y=-58[/tex]

Konichiwa~! (Hello~!) My name is Zalgo and I am here to help you today! In order to turn this into a ration, you need to look at the equation itself and think about how you could do it, which is quite simple. You could do 2:46 or 46:2.

I hope that this helps! :T

"Stay Brainly and stay proud!" - Zalgo

Answer:

Step-by-step explanation:

Twelve

You are correct, but I have a small comment.

As far as I can see, you have both 12 and 13 correct. The short way to do 12 is just to divide 72 into 360

360 / 72 = 5

The more general formula  is 360 / central angle = # of sides.

What the question means is that if your start with a polygon (it is a regular polygon by the way), and rotate it around its center, how many sides does it have in order that when you go through 72 degrees, the figure looks like it did when you started.

If the polygon is completely unmarked, then the idea is that it will look like you haven't done anything to the polygon even though you have rotated it 72 degrees.

The way you did 13 is exactly how it should be done.

Answer:

15+x<_25

Step-by-step explanation:

however much weight the puppy gains (x) can not be greater than 25 but can be equal to 25

Answer:

[tex]15+x\leq 25[/tex]

So, [tex]x\leq 10[/tex]

Step-by-step explanation:

Boston Terriers weigh up to 25 lb.

Suppose a puppy of this breed weighs 15 pounds.

Let the puppy can weigh 'x' pounds more.

So, [tex]x=25-15=10[/tex]

But as it is given the maximum weight can be 25 pounds, so the puppy can weigh a maximum of 10 pounds more.

Given by :

[tex]15+x\leq 25[/tex]

So, [tex]x\leq 10[/tex]

Answer:

#5: 180 paperclips in total.

#6: 126 stamps in total.

#7: Elena should give Lucy 15 colored pencils.

Step-by-step explanation:

This explanation solves each question by setting a single unknown, [tex]x[/tex].

Let [tex]x[/tex] the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

Antonio gives [tex]30[/tex] paperclips to Abby. After that,

Abby now possess twice as many paperclips as Antonio does. In other words,

[tex]2(x - 30) = x + 30[/tex].

By the distributive property:

[tex]2x - 60 = x + 30[/tex].

Substract [tex]x - 60[/tex] from both sides

[tex]x = 30 - (-60) = 90[/tex].

Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.

Similarly, let [tex]x[/tex] be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

After Emily gives [tex]42[/tex] stamps to Jasmine:

Jasmine now possesses twice as many stamps as Emily does. In other words,

[tex]2(x-42) = x+42[/tex].

[tex]x = 42 + 2\times 42 = 126[/tex].

Jasmine used to possess 126 stamps. Now she possesses [tex]126 + 42 = 168[/tex] stamps after receiving [tex]42[/tex] stamps from Emily.

Let the number of pencils that Elena needs to give to Lucy be [tex]x[/tex].

Initially:

After Elena gives [tex]x[/tex] pencils to Lucy:

Elena should now possess four more pencils than Lucy does. In other words,

[tex]\underbrace{60 - x}_{\text{Elena's}} = \underbrace{(26 + x)}_{\text{Lucy's}} +4[/tex].

[tex]2x = 30[/tex].

[tex]x = 15[/tex].