If ∠HJK is 35° and ∠FJI is 95°, what is the measure of ∠KJG?

let x be the capital invested in the 9% account

let y be the capital invested in the 8% account

let j be the interest earned from the 9% account

let k be the interest earned from the 8% account

[tex]j = xi_{1}n \: \: \: (n = 1 \: year)\\ j = x( \frac{9}{100})(1) = 0.09x[/tex]

[tex]k =yi_{2}n \: \: \: \: (n = 1 \: year) \\ k = y( \frac{8}{100} )(1) = 0.08y[/tex]

But the total interest made is 2100 $, hence:

[tex] \: \: \: \: \: \: \: j + k = 2100 \\ 0.09x + 0.08y = 2100[/tex]

And the total capital invested is 25000 $

[tex]x + y = 25000[/tex]

System of 2 equations and two unknowns:

[tex]0.09x + 0.08y = 2100 \\ x + y = 25000 \\ \\ \: \: \: \: (x,y)=(10000,15000)[/tex]

Answer:

1/4

Step-by-step explanation:

First u subtract both sides by 9

12x + 9-9= 4x + 7-9 = 12x = 4x + 2

Then u subtract

12x= 4x - 2

12x - 4x =4x - 2 - 4x=

and this will get u 1/8 but then u simplify and get 1/4

Answer: 24, 26

Step-by-step explanation:

a=first even number. b=second even number

a=b-2

a*3=b*2+20

(b-2)*3=2b+20

3(b-2)=2b+20

3b-6=2b+20

b-6=20

b=26

a=b-2

a=26-2

a=24

24, 26

Answer:

mark me please

Explanation:

If the lesser of two consecutive even integers is tripled, the result is 20 more than twice the grater integer. find the two integers

let the numbers be x & x+2

3x=20+2(x+2)

3x=20+2x+4

3x-2x=24

x=24

The integers are 24 & 26

Order of the given expression into smallest to largest are as follow:

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12} < \frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12}[/tex]

As given in the question,

Given expressions are as follow:

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12},\\\\\frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12}\\\\\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} \\ \\\frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)}[/tex]

Arrange them in the order of smallest to largest by simplifying them,

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12}= \frac{2+4}{24-12\\}[/tex]

          = 0.5

[tex]\frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12}= \frac{4+\sqrt{2} }{12}[/tex]

          =0.45

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} = \frac{2+4}{-48}[/tex]

           = -0.125

[tex]\frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)}= \frac{4+\sqrt{2} }{-48}[/tex]

            = -0.1128

-0.125 < -0.1128 < 0.45 < 0.5

Therefore, order of the given expression into smallest to largest are as follow:

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12} < \frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12}[/tex]

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Considering the cube root of 27, we have that:

a) The correct solution is of 3.

b) The error that Ana likely made is that she considered the cube root as the number that is multiplied by 3 to get a result of 27, not the number that is elevated to three.

The question is that Ana wrote 9 as a solution to the cube root of 27.

The cube root of a number is the number that is elevated by 3 to reach the number, for example:

From the last bullet point, we get the correct answer for item a.

For item b, we have that 9 x 3 = 27, hence the error that Ana likely made is that she considered the cube root as the number that is multiplied by 3 to get a result of 27, not the number that is elevated to three.

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Answer:

Step-by-step explanation:

84.5

Answer:

1575

Step-by-step explanation:

3/8 as a decimal is .375. Multiply 4200 by .375 to get your answer.

Answer: 187 push ups

Step-by-step explanation:

34/2=17 push ups per minute

11 minutes * 17 push ups/1 minute =187 push ups

The width of the rectangle is 14 units and the right option is b 14

Perimeter can be defined as the total distance around an object.

To calculate the width of the rectangle, we use the formula of perimeter.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the width of the rectangle is 14 units and the right option is b 14

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2x+4

substitute x as -6

-12+4= -8

g(-6)=-8

The equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).

Since the directrix y = 1, it shows it is vertical, so we use the equation of the parabola that opens up or down.

( x - h )² = 4p( y - k )

Given the data in the question;

First, we determine the vertex.

The vertex ( h,k ) is half way between the directrix and the focus.

Find the y-coordinate of the vertex using;

y = ( y-coordinate of focus + directrix )/2

y =  (7+1)/2 = 8/2 = 4

The x-coordinate of the vertex is the same as that of the focus 0

Hence, the vertex is ( 0,4 )

Next, we determine the distance p from the focus to the vertex.

p = y-coordinate of focus - y-coordinate of vertex

p = 7 - 4

p = 3

Now, plug the known values into the equation and simplify

( x - h )² = 4p( y - k )

( x - 0 )² = 4(3)( y - 4 )

x² = 12( y - 4 )

Therefore, the equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).

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Answer:

  a = 4

Step-by-step explanation:

You are given an arithmetic sequence with second term 5.5 and fifth term 10. You want to know the first term.

The 2nd term will have 3 times the common difference added to it to make the 5th term. Then that difference can be found from ...

  5.5 +3d = 10 . . . . using 'd' for the common difference

  3d = 4.5

  d = 1.5

The second term (a2) is obtained by adding the common difference (d) to the first term (a1):

  a2 = a1 +d

  5.5 = a1 + 1.5

  4.0 = a1

The value of 'a' is 4.

__

Additional comment

The 'd' we're using here to represent the common difference is not to be confused with the 'd' in the problem statement that represents the fourth term of the list.

The fact that adjacent list members have the same difference is what tells you this is an arithmetic sequence. In terms of the problem statement, you have ...

  {a, b, c, d, e} = {4, 5.5, 7, 8.5, 10}

Here, we have used the more common notation for elements of an arithmetic sequence.

Answer:

$271

Step-by-step explanation:

$741-$199= $542

$542/2= $271

271=p

Irenes $271+ Rochelles $271+199 more than Irene= $741

Irene only raised $271 and rochelle raised 470$

For ΔDEF, Where e=52, f=41 and ∠F=48°. Find all the possible ∠E to the nearest degree.

The possible ∠E to the nearest degree is ∠E=70°

Given that,

ΔDEF with e=52 and f=41 sides of the triangle.

Angle ∠F=48°.

We have to find ∠E=?

By using the Law of sine

The relationship between the sides and angles of non-right (oblique) triangles is known as the Law of Sines. It simply states that for all sides and angles of a given triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same.

If triangle ABC are there with sides a, b, and c then Law of sine is

[tex]\frac{a}{SinA} =\frac{b}{SinB} =\frac{c}{SinC}[/tex]

Now, in the given triangle we have e and f sides so we take

[tex]\frac{SinE}{e}=\frac{SinF}{f}\\[/tex]

Substituting the values of e, f and F

We get,

[tex]\frac{SinE}{52}=\frac{Sin48^\circ}{41}\\ SinE=\frac{Sin48^\circ}{41}\times52\\SinE=\frac{52}{41} \times Sin48^\circ\\SinE=1.268\times 0.743\\SinE=0.942\\E=Sin^{-1}(0.942)\\[/tex]

∠E=70°

Therefore, The possible ∠E to the nearest degree ∠E=70°.

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Answer:448

Step-by-step explanation:None

Answer:

448

Step-by-step explanation:

(-4 × 16)×(-7)

(-64)×(-7)

448

Answer:

1,440

Step-by-step explanation:

London 962

Rio       +118.5%

One percent of 962 is 9.62 you get that by moving the decimal place over one place, multiply by 118.5 to get 1,139.97 there is no partial medals so round to the nearest whole number and you get 1,140.

hope this helped! :) feel free to ask any questions and please mark my answer if it helped you thanks!

Pete will earn $594.83 for one week that he worked for 51 hours

What is the normal hours of work per week?

The number of hours that Pete works normally in any week is 40 hours, beyond the 40 hours, it is regarded as overtime and the overtime hours are paid at one and a half of the normal hourly rate of $11.55

overtime=51.50-40

overtime=11.50

normal earnings=40*$11.55

normal earnings=$462.00

overtime pay=11.50*$11.55

overtime pay=$132.83

total weekly earnings=$462.00+$132.83

total weekly earnings=$594.83

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Answer: 7.93

Step-by-step explanation: I am not sure if this is correct but I really hope it helps.

Answer: R'=(6, -2)

S=(-6,9) ==> S'=(6, -9)

T=(-5,9) ==> T'=(5, -9)

U=(-5,2) ==> U'=(5, -2)

Step-by-step explanation:

When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.

R=(-6, 2) ==> R'=(6, -2)

S=(-6,9) ==> S'=(6, -9)

T=(-5,9) ==> T'=(5, -9)

U=(-5,2) ==> U'=(5, -2)

Solution of the inequality is q> 1/4 and in interval notation is (1/4 , ∞ ).

According to the question we have been given the inequality that is

                3/4q - 2/3q < 5/12q - 1/12

Solving the equation step by step we get

First simplifying 3/4q - 2/3q which will get q/12

Therefore,         q/12 < 5/12q - 1/12

moving all the terms with q on the left hand side we get

                       q/12 - 5/12q < -1/12

                       (q-5q)/12 < -1/12

                          -4q/12 < -1/12

multiplying both sides by 12 we get

                            -4q/12 * 12 < -1/12*12

                                -4q < -1

multiplying -1 both sides we get

                                  4q>1

                                     q >1/4

Hence solution of the inequality we get

                  (1/4 , ∞ )

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Answer:

Step-by-step explanation:

Last week, the typical amount of money spent by kids in the cafeteria ranged from $2.25 to $3.25.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.

A mathematical equation can have many different components, such as coefficients, variables, operators, constants, terms, expressions, and an equal sign. An "=" symbol, as well as terms on both sides, are required when writing an equation.

Given:

Average amount spend = $2.75

Let x be the average dollar amount that students spend.

Then, the equation can be

|x - 2.75| = 0.5

Now, we have two values one is positive and another is negative

x - 2.75 = 0.5 or -(x - 2.75) = 0.5

x = 3.25 or x = 2.25

Hence, Last week, the typical amount of money spent by kids in the cafeteria ranged from $2.25 to $3.25.

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Answer:

Step-by-step explanation:

The number of square units required to fill a square is the area.

Area of a square = side × side

Area of a square = side2 square units

Area of a square field = 479 ft2 [Given]

So the side can be determined by:

Length of a side of the field = √479 = 21.9 feet

Therefore, the length of a side of the field is 21.9 feet.

Answer:

C. They are similar because corresponding sides are proportional.

Step-by-step explanation:

A and B are not are not how you would find similar triangles, so you can rule those answers out. We can also rule out D since the triangles aren't congruent - we can see they have different lengths. This leaves option C.

Here's how to check:

We'll take the ratio of FD:DE, which is 9:12.

9 ÷ 12 = 0.75

The corresponding sides on the second triange are CA:AB, which is 12:16

12 ÷ 16 = 0.75

9:12 = 12:16

The two traingles are similar & have proportional corresponding sides

Answer:

Answer is x=11

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(x−8)+11=17

(2)(x)+(2)(−8)+11=17(Distribute)

2x+−16+11=17

(2x)+(−16+11)=17(Combine Like Terms)

2x+−5=17

2x−5=17

Step 2: Add 5 to both sides.

2x−5+5=17+5

2x=22

Step 3: Divide both sides by 2.

2x/2=22/2

x=11

Answer:

60% increase

Step-by-step explanation:

First: subtract your final value by your starting value

136 - 85 = 51

Second: divide your product from the first step by your starting value

51 ÷ 85 = 0.6

Third: multiply your product from the second step by 100

0.6 x 100 = 60

Step-by-step explanation:

a. 8 × -1 = -8 or -2 × 4 = -8

8 ÷ -1 = -8 or 32 ÷ -4 = -8

b. -3 × 5 = 15 or 15 ×(-1) = -15

45 ÷ -3 = -15 or 225 ÷ -15 = -15

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The car's speed to feet per minute is  80.67ft per second.

What is speed?

1 mile = 5280 feet 

so 55 miles = 55*5280 = 290,400ft 

there are 60 seconds in 1 minute and 60 minutes in 1 hour 

so 1 hour = 60*60 = 3600 seconds 

55mile/1hour = 290400ft/3600 seconds = 80.67ft per second

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Answer:

a: 4

b: 5 is alone, p, -4p and 5p are in the same group, and 7q is alone
c: 2uv squared and -uv squared are in the same group. Everything else is alone.

Step-by-step explanation:

4 is multiplied by y. Kinda self explanatory.

Even though p doesnt have a number before it, it still does. Variables always have coefficients, and if you can't see it, that means it's one.
uv squared is one of the terms, so any number before it makes it part of the group. Everything else is not similar, so you got your answer.

I don't know what grade you are in, but I'm guessing your in a low grade, so sorry if I was unclear.