Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?

Answer:

15

Step-by-step explanation:

The fact angle G and F are equal means the triangle is isosceles triangle. And an isosceles triangle has two equal sides on the opposite sides of the equal angles. Which means x equals HF which is 15.  

Question

What is the value of x?

Answer:

Step-by-step explanation:

this is an isosceles triangle, 2 equal sides and 2 equal angles, so

FH = GH

15 = 15

The unit rate is another way of saying speed, so we divide the distance over the time. We can pick on any row

If we pick row 1, then, speed = distance/time = 90/2 = 45

Row 2 says the same thing: 135/3 = 45

So does row 3: 225/5 = 45

and so on

Because the speed is 45 mph, the unit rate is 45 miles in one hour. The term "unit" implies how much distance can be covered in one unit of time, in this case 1 hour.

You have the correct answer. Nice work.

A general proof for this would be that since Angle A + Angle F + Angle E = 180°, and each of these angles is congruent to some angle inside of Triangle CGH; that CGH would equal 180°.

Interior angles of triangles = 180°, which is common knowledge; unfortunately this isn't an answer choice - so we use the above proof.

F ~= C

A ~= H

E ~= G

So, Angles A and H are congruent would be the correct solution.

Answer:

60

Step-by-step explanation:

If Tonya bought 10 pears and spent a total of $10.00 in expression 0.50a+0.65p represents the total cost of a apples and p pears then Tonya bought 7 apples.

Let's use the information provided to set up an equation and solve for the number of apples (a) that Tonya bought.

Cost of pears (p) = $0.65 each

Cost of apples (a) = $0.50 each

Total cost = $10.00

We are told that Tonya bought 10 pears. So, the cost of 10 pears would be:

Cost of 10 pears = 10 * $0.65 = $6.50

Now, we can set up an equation to represent the total cost of apples and pears:

Total cost = 0.50a + 0.65p

We know that the total cost is $10.00 and the cost of 10 pears is $6.50:

$10.00 = 0.50a + $6.50

Now, let's solve for 'a' (the number of apples):

Subtract $6.50 from both sides:

$10.00 - $6.50 = 0.50a

$3.50 = 0.50a

Now, divide both sides by 0.50 to solve for 'a':

a = $3.50 / $0.50

a = 7

Tonya bought 7 apples.

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Two equations for the purchase prices can be written. Let o and a represent the costs of an orange and an apple, respectively.

... 4o +5a = 3.56

... 3o +4a = 2.76

We can eliminate the o variable by subtracting 3 times the first equation from 4 times the second:

... 4(3o +4a) -3(4o +5a) = 4(2.76) -3(3.56)

... a = 0.36 . . . . simplify

This value can be substituted into either equation to find o. Let's use the first one.

... 4o +5·0.36 = 3.56

... 4o = 1.76 . . . . . . . . . subtract 1.80

... o = 0.44 . . . . . . . . . divide by 4

The cost of an orange is $0.44; the cost of an apple is $0.36.

_____

Comment on the solution

There are perhaps half a dozen different ways to solve a pair of linear equations in two variables. This method isn't necessarily the easiest, but it works. If you have a graphing calculator, quite often it includes matrix operations that will solve this quickly and easily.

Final answer:

The domain restrictions of the expression [tex]g^2[/tex] are the same as the domain restrictions for the variable g.

Explanation:

The domain restrictions of the expression [tex]g^2[/tex], can vary depending on the context in which it is used.

However, in general, the domain restrictions for this expression would be the same as the domain restrictions for the variable g.

This means that any values that make g undefined or result in a complex number would also be restrictions for [tex]g^2.[/tex]

For example, if g cannot be negative due to a square root operation, then the domain restrictions for [tex]g^2[/tex] would also exclude any negative values of g.

[tex]\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}\\-------------------------\\\\\left(\dfrac{w^{15}}{w^5}\right)^4=\left(w^{15-5}\right)^4=\left(w^{10}\right)^4=w^{10\cdot4}=w^{40}\\\\Answer:\ \boxed{\left(\dfrac{w^{15}}{w^5}\right)^4=w^{40}}[/tex]

[tex]\displaystyle\\(x-4)^2=49\\\\(x-4)^2-49=0\\\\(x-4)^2-7^2=0\\\\(x-4-7)(x-4+7)=0\\\\(x-11)(x+3)=0\\\\x-11 = 0~~~\text{or}~~~x+3=0\\\\x-11=0~~~\implies~~~\boxed{x_1=11}\\\\x+3=0~~~\implies~~~\boxed{x_2=-3}\\\\\boxed{\bf The~solutions~are:~~x =11~~\text{or}~~x =-3}[/tex]

Answer:

Since, KLMN is a parallelogram, then by the property of parallelogram that opposite angles of a parallelogram is equal, therefore ∠N=∠L and ∠M=∠K.

Step-by-step explanation:

Answer:

It is followed by properties of parallelogram and the proof is explained in step-by-step solution.

Step-by-step explanation:  

Given a parallelogram KLMN

Parallelogram is a quadrilateral with parallel opposite sides.  

To Prove: ∠N≅∠L and ∠M≅∠K  

In Parallelogram KLMN the opposite sides are parallel therefore, the opposite angles are vertical angles. And the vertical angles are always equal and congruent. Hence,  

∠N≅∠L and ∠M≅∠K  

For any quadrilateral sum of all angles equal to 360°  

m∠K + m∠L + m∠M + m∠N = 360°  

Now given quadrilateral is parallelogram therefore opposite angles are equal. So, we can write m∠L = m∠N, m∠M = m∠K  

⇒ m∠K + m∠N + m∠K + m∠N = 360°  

2 m∠K + 2 m∠N = 360°  

m∠K + m∠N = 180°  

For the same parallelogram, because opposite sides are equal therefore use m∠K = m∠L, m∠N = m∠M using above equation, we get  

m∠L + m∠M = 180°  

Because m∠M = m∠K  

m∠K + m∠L = 180°  

Same Side Interior Angles Theorem states that if the two parallel lines intersect or cut by a transversal then the interior angles on the same side are supplementary that means their sum is equal to 180°  

Hence, by above theorem m∠K + m∠N = 180°  

& m∠K + m∠L = 180°  

By above two equations, we get  

m∠K + m∠N = m∠K + m∠L  

because m∠K = m∠M & ∠N = ∠L  

⇒ m∠L + m∠M = m∠K + m∠L  

Because opposite angles of a parallelogram are alternate angles therefore are equal. hence,  

m∠N = m∠L  

m∠M = m∠K  

Angle congruency postulate  

Opposite angles of parallelogram are vertical angles and the vertical angles are congruent as well as equal.  

∠N≅∠L and ∠M≅∠K  

Substitution Property of equality states that if one angle is equal to another angle the one can be substituted in the place of another that means if ∠M=∠K then we can substituted ∠K in place of ∠M  

Transitive property of congruence states that if if the two angles or segments or triangles are congruent to third then they are congruent to each other.  

Subtraction Property of Equality states that if if two sides of any equation are equal then subtraction of same value from both sides results in equality of equation.  

Parallel lines are those lines which do not intersect or cut each other at the end.  

Parallelogram is a quadrilateral have opposite sides equal and parallel.  

:

Answer:The value of Zlatan's house has increased be 7%. His house is now valued at 749,000. Work out the value of the house before the increase.

Don't worry! I got you! just whip out a calculator and take 749,000 and tomes it by 0.07, which is 7%. That gives you 52,430, which means you take 749,000 and subtract 52430, which ultimately give you an ANSWER of (696,570) Hope that helps!

Step-by-step explanation:

Answer:

$ 700,000

Step-by-step explanation:

Let x be the original value of the Zlatan's house,

After increasing the value of the house by 7%,

New cost of his house = (100+7)% of x

= 107% of x

[tex]=\frac{107x}{100}[/tex]

= 1.07x

According to the question,

[tex]1.07x = 749,000[/tex]

[tex]x=\frac{749000}{1.07}=\$ 700000[/tex]

Hence, his house value would be $ 700000  before the increase.

Answer:

B Twelve students answered Mr. Chiu’s question.

C Three people studied for two hours.

F Four people studied for four or more hours.

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

The information that can be missing from the dot plot is the scale and data points.

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.

Elias dot plot may not have a distinct scale on the axes, which makes it challenging to identify the precise values or quantities being displayed. This is based on the fundamental idea of a dot plot. A scale offers the required context for correctly analysing the data by, among other things, specifying the measurement intervals or units that were employed.

Furthermore, certain data points, such as the number of tropical fish in each tank or the exact values being displayed, may be absent from the dot plot. It would be difficult to evaluate the dot plot or make inferences from it without the actual data points. Overall, it is impossible to pinpoint exactly what information may be lacking without further detailed details concerning Elias' dot plot.

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complete question:

Elias made a dot plot that shows the number of tropical fish contained in the 14 aquariums at the pet store. What information is missing from Elias dot plot?

Answer:

A is smaller.

Step-by-step explanation:

SAc of cylindrical container:

Diameter of base: 60 mm

Radius of base: 30 mm

Height of cylinder: 240 mm

SAc = lateral area + area of two bases

SAc = (pi)dh + 2(pi)r^2

SAc = (pi)(60 mm)(240 mm) + 2(pi)(30 mm)^2

SAc = 14,400(pi) mm^2 + 1,800(pi) mm^2

SAc = 16,200(pi) mm^2 which approximately equal to 50,868 mm^2

SAp of prism:

Rectangular prism with L = 120 mm, W = 120 mm, H = 0 mm

SAp = 2(LW + LH + WH)

SAp = 2(120 mm * 120 mm + 120 mm * 60 mm + 120 mm * 60 mm)

SAp = 2(14,400 mm^2 + 7,200 mm^2 + 7200 mm^2)

SAp = 2(28,800 mm^2)

SAp = 57,600 mm^2

The total surface are of the prism is greater than the total surface area of the cylinder.

Answer:

The vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5). The graph of image and preimage is shown below.

Step-by-step explanation:

From the given figure it is noticed that the vertices of  triangle ABC are A(0,0), B(1,5) and C(-4,5).

If a figure rotated at 180º about the origin, then

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

The vertices of image are

[tex]A(0,0)\rightarrow A'(0,0)[/tex]

[tex]B(1,5)\rightarrow B'(-1,-5)[/tex]

[tex]C(-4,5)\rightarrow C'(4,-5)[/tex]

Therefore the vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5).

The graph of image and preimage is shown below.

Answer: the correct answer is the third option

Answer:

C. (-3.6, 17)

Step-by-step explanation:

The relative maximum occurs at an x coordinate between -3 and -4. The relative maximum is between 15 and 20. The best approximation is

C. (-3.6, 17)

Answer:

c. (-3.6, 17)

Step-by-step explanation:

The relative maximum is the maximum in a region.  The maximum between -6 and  is found and x=-3.6 and the value is 17.  So x=-3.6 and y=17

Answer:

65,550.

Step-by-step explanation:  

We have been given that the population of a town increased by 15% in 2016, and decreased by 5% in 2017.

Since an exponential is in form: [tex]a*b^x[/tex].  

For growth b=(1+r), where r in rate in decimal form.  

For decrease b=(1-r), where r in rate in decimal form.

[tex]15\text{ percent}=\frac{15}{100}=0.15[/tex]

Let us find the population increase in 2015.

[tex]\text{Population at the end of year 2016}= 60,000*(1+0.15)^1[/tex]  

[tex]\text{Population at the end of year 2016}= 60,000*(1.15)[/tex]  

[tex]\text{Population at the end of year 2016}= 69,000[/tex]

Therefore, the population at the end of year 2016 will be 69,000.

Now let us find population decrease of 5% in year 2017.

[tex]15\text{ percent}=\frac{5}{100}=0.05[/tex]

[tex]\text{Population at the end of year 2017}= 60,000*(1-0.05)^1[/tex]  

[tex]\text{Population at the end of year 2017}= 60,000*(0.95)[/tex]  

[tex]\text{Population at the end of year 2017}= 65,550[/tex]  

Therefore, the population at the end of year 2017 will be 65,550.

Answer:

None

Step-by-step explanation:

The center of the ellipse is at  (2,  4)

The length of the x axis is  a=  (8-2) =6

The length of the y axis is b=(16-4) = 12

The formula for an ellipse is

(x-h) ^2       (y-k)^2

----------- + -------------- = 1^2

a^2              b^2

where (h,k) is the center

and a and b are the  lengths of the major and minor axes

(x-2) ^2       (y-4)^2

----------- + -------------- = 1

6^2              12^2

 none of your choices have b>a  and for the ellipse to be vertical b>a

Answer:

y=6+x

Step-by-step explanation:

2+6=8              6+6=12

Answer:

tan C = 1/2

Step-by-step explanation:

The tan function in a right triangle is the opposite side over the adjacent side

tan C = 11/22

We can divide the top and bottom by 11

tan C = 1/2

Answer: Tan(C) = 1/2

Step-by-step explanation:

For a triangle rectangle, we have the relation, for an angle θ.

Tan(θ) = Opposite cathetus/Adjacent catethus.

Here, the opposite cathetus to C is equal to 11 units

The adjacent cathetus to C is 22 units.

Then we have Tan(C) = 11/22 = 1/2

and we can not simplify it anymore, so this is the answer.

Answer:

$4.72

Step-by-step explanation:

16.79+28.49=45.28

50-45.28=4.72

We know that, Volume of a Rectangular Prism is given by :

✿  {Length × Width × Height}

Given : The Length of Rectangular Prism = 5.5

Given : The Width of Rectangular Prism = 6

Given : The Height of Rectangular Prism = 3

⇒ The Volume of given Rectangular Prism = {5.5 × 6 × 3}

⇒ The Volume of given Rectangular Prism = 99

The Kansas City Royals won approximately 78.57% of their playoff games in 2014.

To find the percentage of games won by the Kansas City Royals, we divide the number of games they won by the total number of games played and then multiply by 100. In this case, the Royals won 11 out of 14 playoff games in 2014. So the percentage of games they won is:

Percentage = (Number of games won / Total number of games) x 100

= (11 / 14) x 100 = 78.57%

Therefore, the Royals won approximately 78.57% of their playoff games in 2014.

Answer:

B. Rhombus

Step-by-step explanation:

A rombus has four congruent sides and has 2 equal pairs of angles, the rhombus has 4 equal sidesd that are conected by 4 suplemmentary angles between them, in the end the sum of the inner angles is 360 like in every polygon.

The equation 4t = 70 can be solved by dividing both sides by 4, yielding t = 17.5. This is not a quadratic equation, so the quadratic formula is not required.

To solve the equation 4t = 70 and approximate the value of t to four decimal places, we will first perform a simple algebraic operation. Divide both sides of the equation by 4 to isolate t.

t = 70 / 4
t = 17.5

This is a straightforward equation, but we should be cautious not to mix it up with a quadratic equation, which would require the use of the quadratic formula. The quadratic formula is used for equations of the form at² + bt + c = 0 and would look like this:

-b ± √b² - 4ac over 2a.

Given that the original equation provided is not quadratic, we do not need this formula for our current problem. The correct solution for our equation is t = 17.5.

Final answer:

The question is about estimating the number of ice cream cones sold at 106 degrees Fahrenheit based on a set of data correlating temperature with sales. An educated guess, without exact calculations, suggests that at least 649 cones might be sold, based on the pattern observed in the data provided.

Explanation:

The student's question touches on the relationship between temperature and the number of ice cream cones sold. Looking at the data provided, there seems to be a positive correlation: as temperature increases, so does the number of cones sold.

Based on the steady increase in the number of cones sold with each increase in temperature, it is reasonable to assume that if the temperature were to increase from 99 degrees (which correlated with 576 cones sold) to 106 degrees, the number of cones sold would increase by at least the same increment as previous temperature rises, if not more.

If we take the difference between 94 degrees and 99 degrees, which is an increase in 5 degrees and corresponds to an increase of 576 - 503 = 73 cones, we could estimate that at 106 degrees, the shop might sell at least 73 more cones than they did at 99 degrees.

This would yield an estimate of 576 + 73 = 649 cones as a conservative minimum estimate.