23 more than the product of 7 and a number

Answer:

The third integer is 27

Step-by-step explanation:

Given

Represent the consecutive odd numbers with [tex]T_1, T_2; and\ T_3[/tex]

Since they are consecutive odds, then

[tex]T_2 = 2 + T_1[/tex]

[tex]T_3 = 2 + T_2[/tex]

From the first statement in the question, we have that

[tex]T_1 + T_3 = 5 T_2 - 75[/tex]

Required

Find the third integer

Recall that

Substitute [tex]T_2 = 2 + T_1[/tex] in [tex]T_3 = 2 + T_2[/tex]

[tex]T_3 = 2 + 2 + T_1[/tex]

[tex]T_3 = 4 + T_1[/tex]

Substitute [tex]T_3 = 4 + T_1[/tex] and [tex]T_2 = 2 + T_1[/tex] in [tex]T_1 + T_3 = 5 T_2 - 75[/tex]

[tex]T_1 + 4 + T_1 = 5(2 + T_1) - 75[/tex]

Open Brackets

[tex]T_1 + 4 + T_1 = 10 + 5T_1 - 75[/tex]

Collect like terms

[tex]T_1 + T_1 + 4 = 5T_1 - 75 + 10[/tex]

[tex]2T_1 + 4 = 5T_1 - 65[/tex]

Collect like terms

[tex]2T_1 - 5T_1 = - 65 - 4[/tex]

[tex]-3T_1 = - 69[/tex]

Divide both sides by -3

[tex]\frac{-3T_1}{-3} = \frac{- 69}{-3}[/tex]

[tex]T_1 = 23[/tex]

Recall that [tex]T_3 = 4 + T_1[/tex]

[tex]T_3 = 4 + 23[/tex]

[tex]T_3 = 27[/tex]

The third integer is 27

Answer: Mica spent $70.65

Step-by-step explanation:

Mica's bank balance before shopping = $22.50

Mica's bank balance after shopping = - $48.15

Mica's spending could be calculated by:

Difference between initial and final bank balance.

Hence,

[(Bank balance before shopping - (bank balance after shopping)]

[$22.50 - (-$48.15)]

= $22.50 + 48.15

= $70.65

Answer:19.1

Step-by-step explanation:

Answer:

B. 46.1 in

Step-by-step explanation:

First, we must find the hypotenuse of the triangle.

Since this is a right triangle, we can use Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs and c is the hypotenuse.

13 and 14 are the legs, because they form the right angle. x is the hypotenuse because it is opposite the right angle.

13^2+14^2=x^2

Evaluate each exponent.

13^2=13*13=169

14^2=14*14=196

169+196=x^2

Add 169 and 96

365=x^2

Take the square root of both sides.

√365=√x^2

√365=x

19.1049732=x

Round to the nearest tenth.

19.1=x

The hypotenuse is 19.1 inches

Now, find the perimeter. Add up all the sides of the triangle: the legs (13 in and 14 in) and the hypotenuse (19.1 in)

13 in +14 in +19.1 in

46.1 in

The perimeter is 46.1 inches and B is correct.

Answer:

Her grocery bill is $4.62

Step-by-step explanation:

The first step is to multiply 6 and .43 to get how much it was for all of the apples.

Then the next step is to do the same thing with the oranges.

Then the last step is to add the two together.

Answer:

$4.62

Step-by-step explanation:

Answer:

The answer is option D.

I hope this helps.

Answer:

y = 2/7x +11

3x-4y = -24

Step-by-step explanation:

We would want to use substitute on the last set of equations since the first equation is already solved for y.  It is easy to substitute for y in the second equation

Answer:

Total weight = 70.5 kg

Step-by-step explanation:

Rectangular frame is made from 5 straight pieces of metal. One of them goes through the diagonal of the rectangle.

2 pieces form the length of the rectangular frame, hence, they have a length of 12 m each

2 pieces from the width of the rectangular frame, hence, they a length of 5 m each

To find the length of the diagonal, we can use Pythagoras Theorem:

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = 5² + 12²

Hypotenuse² = 169²

Hypotenuse = 13

Hence, the length of the piece of metal placed at the diagonal is 13cm

Find the sum of all lengths of the metal pieces.

Total length = 12 + 12 + 5 + 5 + 13

Total length = 47 m

Total weight = 1.5 × Total length

Total weight = 1.5 kg/m × 47m

Total weight = 70.5 kg

The total weight of the metal in the frame is 70.5 kg

If a rectangular frame is made from 5 straight pieces of metal, with a length of 5m and a width of 12m

Get the diagonal

[tex]d^2= 5^2 + 12^2\\d^2 = 25 + 144\\d^2 = 169\\d= 13m[/tex]

Get the perimeter of the rectangular frame:

Perimeter of the frame = 2(5 + 12) + 13

Perimeter of the frame = 2(17) + 13

Perimeter of the frame = 34 + 13

Perimeter of the frame = 47m

If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:

Total weight = 47 * 1.5

Total weight = 70.5kg

Hence the total weight of the metal in the frame is 70.5 kg

Learn more here: https://brainly.com/question/10452031

Answer:

The solution is (-17,80.5) and (1,8.5)

Step-by-step explanation:

Equation 1 : [tex]y=\frac{1}{2}x^2+4x+4[/tex]

Equation 2: [tex]y = -4x+12.5[/tex]

Substitute the value of y from equation 2 in equation 1

Equation 1 : [tex]y=\frac{1}{2}x^2+4x+4[/tex]

After substitution :

[tex]-4x+12.5=\frac{1}{2}x^2+4x+4\\\frac{1}{2}x^2+8x+4-12.5=0\\\frac{1}{2}x^2+8x-8.5=0\\x^2+16x+17=0\\x=-17,2[/tex]

Substitute the value of x = -17

y = -4x+12.5

y = -4(-17)+12.5

y=80.5

Substitute the value of x = 1

y = -4(1)+12.5

y=8.5

Hence the solution is (-17,80.5) and (1,8.5)

Answer:

The answer is given below

Step-by-step explanation:

From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.

The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2

∠BYZ and ∠DZY are interior angles.

∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)

∠BYZ/2 + ∠DZY/2 = 180/2

∠BYZ/2 + ∠DZY/2 = 90°

In ΔOYZ:

∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).

But  ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2

∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180

90 + ∠YOZ = 180

∠YOZ = 180 - 90

∠YOZ = 90°

Therefore Angle bisectors of the same side interior angles are perpendicular.

Answer:

70.15 ft²

Step-by-step explanation:

The figure consists of two adjacent equilateral triangles (all angles are 60 degrees and all outer edges are 9 ft).

If we focus on one of these equilateral triangles, we can get the final area by multiplying the area of that one triangle by 2.

The formula for the area of a triangle is (1/2)(base)(height).  Remembering to multiply this by 2, we get

area of figure = (base)(height)

                                             √3

                       = (9 ft)(9 ft)(--------) = (81 ft²)(1.732) = 70.15 ft²

                                               2

Answer:

Answer:

The y in the second equation

Step-by-step explanation:

hope this helps

Answer:a x=3 y=-4

Step-by-step explanation:

Step-by-step explanation:To find the interest accumulated over a period of time you use:

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

with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.

A = 2000

P = 1500

r = 0.035

n=1

Thus you get:

2000 = 1500 (1+0.035)^t

Divide by 1500:

(4/3) = (1.035)^t

Apply "ln" on both sides:

ln(4/3) = t*ln(1.035)

Calculate the logarithms:

0.28768 = t*0.03440

Divide by 0.03440 on both sides:

t = 8.36 years

So after approximately 8 years and 5 month you will have $2000 or more in the account.

Answer:

Answer:

b. 100

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph of this function is that of a parabola that opens down (due to the negative coefficient of t^2).  The axis of symmetry is

        -b          -100

x = --------- = ----------- = 50/16 = 25/8.

        2a        2(-16)

The y value of the vertex is h(25/8) = -16(25/8)^2 + 100(25/8) + 10, or 166/25.

The largest value this function can take on is 166/25.  Thus, the range is

(-infinity, 166/25).

Since the given function is a polynomial, the domain consists of all real numbers.

Answer:

Step-by-step explanation:

Find and compare the unit costs of the two different bottle sizes.

First:  

$2.79/(6 oz) = $0.465/oz

Second:

$10.89/(14 oz) = $0.778/oz

Clearly, the larger (14 oz) bottle is a much better buy

Answer: 14oz bottle for 10.89

Step-by-step explanation:

Did it before

Answer:

option 2 is correct ans. it can be solved by substitution method.

Answer:

A. Positive

Step-by-step explanation:

Since 48 is way larger than 39, we know that if we subtract 39 from 48, we will still get a positive number.

Answer:

A. Positive

Step-by-step explanation:

Im not very good at explaining. I hope I helped :)

Answer:

correct answer is 2800.

Step-by-step explanation:

You take the area of the square which is 20x20 = 400.

There is 5 squares 400x5 = 2000

There is 4 triangles--which is 1/2 the area of 1 square (In this case).

One triangle = 200

200x4 = 800

2000 + 800 = 2800

Answer:

Step-by-step explanation:

550

g(x) = (x - 5)^2 + 2x^3

At the root this function is equal to 0

(x - 5)^2 + 2x^3= 0

Rearrange:

(x - 5)^2 = -2x^3

Now if you plot these two functions you need to check how many times they intersect. For this you do not need to be precise just scetch approximately.

If you do that, you will see that they meet once. I cannot really use this site to plot, but you can use other tools for that if you do not know how to do it.

Answer:

270 ft square

Step-by-step explanation:

10cm * 1.5ft = 15 ft

12cm * 1.5ft = 18ft

18ft * 15ft = 270ft square

Answer:

270 sq ft

Step-by-step explanation:

Answer:

Since ∠E ≅ ∠A and ∠D ≅ ∠B, the answer is ΔABC ~ ΔEDF.

Answer:

option 2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Step-by-step explanation:

1.32:24

32/8:24/8

4:3

2.20:32

20/4:32/4

5:8

3.24:76

24/4:76/4

6:19

4.24:32:20

24/4:32/4:20/4

6:8:5

Answer:

The density of the material must be at least 1.5 g/cm³.

Step-by-step explanation:

22. 30 degrees because line DB bisects(meaning cuts in half) angle ABC so DBC should be 30 degrees because 30+30 is 60 which is what angle ABC is.

23. 60 degrees because if we assume that it is a parallelogramand that the opposite angle are congruent.

24. 120 degrees because a quadrilatteral has sides that will equal to 360 degrees, and I said that a parallelogram will have its opposite angles congruent we take away 120 from 360 (from the previous angles ABC and BCD) we end up with 240, we divide 240 by 2 and end up with 120 degrees

25. 60 degrees. I found that angle DCB is 120 degrees so angles DCB and DCE are supplementary(add up to 180 degrees) and we subtract 120 from 180 which is 60 degrees.

26. 60 degrees vertical to angle DCE.

27. 120 degrees supplementary to DCE

I hope this helps you

Answer:

3  -√5

Step-by-step explanation:

(√5 + 1) / (2 + √5)

Multiply top and bottom of the fraction by the conjugate of 2 + √5 which is  2 - √5.

By doing this we rationalise the denominator:

= (√5 + 1 ) *  ( 2 - √5) /  (2 + √5)(2 - √5)

= (√5 + 1 ) *  ( 2 - √5)/ (4 - 2√5 + 2√5 - 5)

= (2√5 - 5 + 2 - √5) / (4 - 5)

= (√5 - 3) / -1

= 3  -√5

Answer:

$252

Step-by-step explanation:

This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.

Jan's " give away " = Ami + 36, Jan - 108, Toy + 72

Toy's " give away " = Ami + 72, Jan + 36, Toy - 108

Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.

144 + 72 + 36 = 252 dollars ( in total )

Answer:

The answer is 252

Step-by-step explanation:

Answer:

WORDS: The value of x is 15.

EQUATION: x = 15

Step-by-step explanation:

1. AB is a straight line therefore angles AOF, FOG, and GOB total 180º

2. If ∠FOG = 90º, AOF + GOB = 90º by subtraction & substitution property

3. 5x - 15 + 2x = 90 (now solve) --> by substitution

4. 7x - 15 = 90 --> by C.L.T. or Combine Like Terms

5. 7x = 105 --> by C.L.T. or Combine Like Terms

6. x = 15 --> by inverse operations (division)

Hope this helps!

Answer:

v=20, w=80

Step-by-step explanation:

First, we can find v by determining that angle 5v and angle 4v and supplementary to each other. This means that their sum adds up to 180 degrees.

5v + 4v=180

9v=180

v=20

We also know 4v is equivalent to w.

4(20)=w

w=80

Answer:

Step-by-step explanation:

5v + 4v = 180   {co-interior angles}

9v = 180

v = 180/9

v = 20

Angles opposite to equal sides are equal.

So, w = 4v

      w = 4*20

      w = 80