Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quarters does he have

Answer:

68

Step-by-step explanation:

48+2+20

Answer:

There are no real number solutions to this question.

The statement which is true for the equation[tex]\sqrt{2x-1} =-1[/tex] is option C which is that x=1.

It is a relationship between variables and it can be in the form of one variable also.

We have been given [tex]\sqrt{2x-1} =-1[/tex]

squaring both sides we get

2x-1=1

2x=1+1

2x=2

x=1

Hence the solution of the equation is x=1.

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Answer:

production cost f(x), in dollars, for x number of units produced by company 1:

f(x) = 0.05x^2 − 7x + 300

2) Table that represents the production cost g(x), in dollars, for x number of units produced by company 2:

x        g(x)

0.6     899.58

0.8     899.52

1        899.50

1.2     899.52

1.4     899.58

3) Comparison: do a table for f(x) with the same x-values of the table for g(x).

x            f(x) = 0.05x^2 − 7x + 300    g(x)

0.6         295.818                               899.58

0.8         294.432                               899.52

1            293.05                                 899.50

1.2         291.672                               899.52

1.4          290.298                              899.58

As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.

The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).

Answer: Based on the given information, the minimum production cost for company 2 is greater.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

x² + 10x + 14 = - 7 ( subtract 14 from both sides )

x² + 10x = - 21

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = - 21 + 25

(x + 5)² = 4 ( take the square root of both sides )

x + 5 = ± 2 ( subtract 5 from both sides )

x = - 5 ± 2

x = - 5 - 2 = - 7, or x = - 5 + 2 = - 3

-------------------------------------------------

The equation can also be solved by factoring

x² + 10x + 14 = - 7 ( add 7 to both sides )

x² + 10x + 21 = 0 ← in standard form

(x + 7)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 3 = 0 ⇒ x = - 3

Answer:

Perimeter of Rhombus = 104 inches  

Step-by-step explanation:

To find the Perimeter of Rhombus we use the formula

Perimeter of rhombus = 4*Length

We need to find the length of rhombus.

if the rhombus has diagonals, it makes four right angled triangles (as shown in figure).

Since 4 triangles are made so, each side of triangle is half of the length of the diagonal.

In our case: Length of diagonals are: 20 and 48

but the Length of sides of triangle will be: 10 and 24

To find the side of rhombus, we can use Pythgoras theorem since the triangles are right angled.

c² = a²+b²

c² = (10)² + (24)²

c² = 100 + 576

c² = 676

√c²= √676

c = 26

So, the length of side of rhombus is 26 inches

Perimeter = 4*length

                = 4*26

                = 104 inches

Perimeter of Rhombus = 104 inches.  

The length of the perimeter of the rhombus is 104 inches.

To find the perimeter of a rhombus with given diagonal lengths of 20 inches and 48 inches, we can use the properties of rhombuses:

Step 1. Relationship between diagonals in a rhombus:

The diagonals in a rhombus cut each other at right angles. Let the diagonal lengths be [tex]\( d_1 \)[/tex] and [tex]\( d_2 \)[/tex].

Step 2. Formula to find side length from diagonals:

The following formula can be used to find the side length ( s ) of a rhombus:

[tex]\[ s = \frac{1}{2} \sqrt{d_1^2 + d_2^2} \][/tex]

where [tex]\( d_1 = 20 \)[/tex] inches and [tex]\( d_2 = 48 \)[/tex] inches.

Step 3. Calculate the side length:

[tex]\[ s = \frac{1}{2} \sqrt{20^2 + 48^2} \][/tex]

[tex]\[ s = \frac{1}{2} \sqrt{400 + 2304} \][/tex]

[tex]\[ s = \frac{1}{2} \sqrt{2704} \][/tex]

[tex]\[ s = \frac{1}{2} \times 52 = 26 \text{ inches} \][/tex]

Step 4. Calculate the perimeter:

The perimeter ( P ) of a rhombus, with all sides equal, is determined by:

[tex]\[ P = 4 \times s = 4 \times 26 = 104 \text{ inches} \][/tex]

Therefore, the length of the perimeter of the rhombus is 104 inches.

For this case we have that by definition of trigonometric relations of a rectangular triangle that, the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle.

That is to say:

[tex]Sin (30) = \frac {IR} {14}[/tex]

We clear the length of the leg:

[tex]IR = 14 * sin (30)\\IR = 14 * \frac {1} {2}\\IR = 7 \ in[/tex]

Answer:

[tex]IR = 7 \ in[/tex]

Consider x as the missing number of hours, so 10x + 25(initial hour) and the total of the rental is $75

10x + 25 = $75

Answer

B

Answer:

From greatest to least is  23:24 , 11:12, 7:8

Step-by-step explanation:

Hope this helps!!!

Answer:

The length of the other leg is [tex]3.21\ units[/tex]

Step-by-step explanation:

I will assume that the triangle is a right triangle

In a right triangle the legs are perpendicular

so

The area of a right triangle is equal to

[tex]A=\frac{1}{2}(a)(b)[/tex]

where

a and b are the legs of the triangle

In this problem we have

[tex]a=39.2\ units[/tex]

[tex]A=63\ units^{2}[/tex]

substitute the values

[tex]63=\frac{1}{2}(39.2)(b)[/tex]

[tex]126=(39.2)(b)[/tex]

[tex]b=126/(39.2)=3.21\ units[/tex]

Answer:

The correct answer is third option

The sum of any number and its opposite is 0

Step-by-step explanation:

It is given an expression,

8.29 * (-5.62 + 5.62)/5.62

To find the correct reason

Here - 5.62 + 5.62 = 0

5.62 is opposite to - 5.62

because sum of a number and its opposite is 0.

Therefore the correct answer is third option.

The sum of any number and its opposite is 0

The answer is A, Angles in an equilateral triangle are congruent.

Which fact would help you to solve for x in the diagram shown?

A) Angles in an equilateral triangle are congruent.  

Answer:

7x-y=61

Step-by-step explanation:

The standard form is Ax+By=C.

Let's simplify the equation first.

1. Distribute: y+5=7x-56

2. Subtract 5: y=7x-61

3. Arrange into standard form: 7x-y=61

Answer

-7x+y=-61

Its the same as 7x-y=61, but in a different form

ANSWER

See below

EXPLANATION

The given point (-3,1) lies in the second quadrant.

In this quadrant only sine is positive.

The length of the hypotenuse formed by the right angle triangle is

[tex] {h}^{2} = {3}^{2} + {1}^{2} [/tex]

[tex] {h}^{2} = 9 + 1[/tex]

[tex]{h}^{2} = 10[/tex]

[tex]h = \sqrt{10} [/tex]

The side opposite to θ, is 1 units.

The adjacent side is 3 units.

[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin( \theta) = \frac{1}{ \sqrt{10} } = \frac{ \sqrt{10} }{10} [/tex]

[tex]\cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = - \frac{3}{ \sqrt{10} } = - \frac{3 \sqrt{10} }{10} [/tex]

[tex] \tan( \theta) = - \frac{opposite}{adjacent} [/tex]

[tex]\tan( \theta) = - \frac{1}{3} [/tex]

The values of sine, cosine and tangent of θ are; 1/√10, -3/√10 and -1/3 respectively.

From the task content, it follows from Pythagoras theorem that;

On this note;

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Answer:

C

Step-by-step explanation:

Using the rules of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

Hence

[tex]7^{-5/6-7/6}[/tex] = [tex]7^{-\frac{12}{6} }[/tex] = [tex]7^{-2}[/tex], then

[tex]7^{-2}[/tex] = [tex]\frac{1}{7^{2} }[/tex] = [tex]\frac{1}{49}[/tex] → C

ANSWER

C. 1/49

EXPLANATION

The given expression is

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } [/tex]

Recall that:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply this product rule of exponents to get:

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{5}{6} + - \frac{7}{6} } [/tex]

This implies that:

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{12}{6} } [/tex]

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - 2} [/tex]

Recall again that:

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

We apply this rule to get:

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{ {7}^{2} } [/tex]

This simplifies to:

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{49} [/tex]

Answer:

X= -13

Step-by-step explanation:

Your first goal is to get all the X’s to one side of the equation.

So:

3x - 5 = 9x + 8 - 5x

+5x +5x

8x - 5 = 9x + 8

-9x -9x

-1x - 5 = 8

Now that you have all the X variables simplified and on one side, you make sure all of you constant terms are on the other side.

-1x - 5 = 8

+5 +5

-1x = 13

Because you can’t have a negative X, you divide the entire equation by -1.

-1x = 13

-1

x = -13

Dividing by -1 will give you the inverse of the equation which is positive one x equals negative thirteen.

Answer:

Step-by-step explanation:

7/8 0r 0.875

y = -5x + 24

y = 4x - 21

Since both of these equations are equal to Y, theyre equal to each other.

So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.

-5x + 24 = 4x - 21

Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:

-5x + 24 - 24 = 4x - 21 - 24

-5x = 4x - 45

Now we subtract 4x from both sides so the 4x shift to the other side

-5x - 4x = 4x - 4x - 45

-9x = -45

Finally divide both sides by -9 so x is by itself

(-9)÷(-9x) = -(45)÷(-9)

x = 5

Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.

Now apply x = 5 to either of the initial equations to find the value of Y

y = -5x + 24 or y = 4x - 21

(I'll do both but u only need one)

y = -5(5) + 24

y = -25 + 24

y = -1

y = 4(5) - 21

y = 20 - 21

y = -1

Either way, X is 5 and Y is -1

Answer (5, -1)

Final answer:

The solution to the system of equations is (5, -1), matching option b. This is found by setting both equations equal to each other, combining like terms, solving for x, and then using that value to find y.

Explanation:

To solve the system of equations, set the two equations equal to each other since they both equal y:

y = -5x + 24
y = 4x - 21

Now equate them:

-5x + 24 = 4x - 21

Add 5x to both sides:

24 = 9x - 21

Add 21 to both sides:

45 = 9x

Now divide by 9 to solve for x:

x = 5

Substitute x back into either original equation to find y:

y = -5(5) + 24
y = -25 + 24
y = -1

The solution is (5, -1), which corresponds to option b.

To check the solution, we can substitute x = 5 into both of the original equations to verify that they are true. For the first equation:

-5(5) + 24 = -25 + 24 = -1

For the second equation:

4(5) - 21 = 20 - 21 = -1

Since both substitutions lead to an identity, the solution is correct. The final answer is (5, -1), or option b.

Answer:

154 adults 94kids

Step-by-step explanation:

Answer:

20% of the number 40 is 8

20% x 40=800 divide 100 =8

Answer:

[tex]y=(2/3)x[/tex]

The graph in the attached figure

Step-by-step explanation:

Let

x-----> the number of pints

y----> the number of servings

For x=3 pints, y=2 servings

This is a proportional variation

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

so

The linear equation is equal to

[tex]y=(2/3)x[/tex]

The graph in the attached figure

Answer:

The graph is attached below

Step-by-step explanation:

A refreshment stand makes 2 large servings of frozen yogurt from 3 pints.

Equation of the line is y=mx+b

where m is the slope and b is the y intercept

2 large serving from 3 pints

So the servings over pints is 2/3

[tex]slope = \frac{2}{3}[/tex]

The y intercept is (0,0). the value of b is 0

We got m=2/3 and b=0

The equation of the line is

[tex]y=\frac{2}{3}x+0[/tex]

[tex]y=\frac{2}{3}x[/tex]

Now make a table. Assume some number for x  and find out y

x            y

0            0

3             2

6             4

Now make a graph using points (0,0) (3,2) and (6,4)

Answer:

c. y=-3x

Step-by-step explanation:

Plug in x=0 and y=0.

0=-3(0)

0=0...the origin

Answer:

Both Scott and Tara have responded correctly.

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

A=(1/2)[b1+b2]h

we have

b1=16 cm

b2=24 cm

h=8 cm -----> Note The height is 8 cm instead of 18 cm

substitute

A=(1/2)[16+24](8)

A=160 cm²

Verify Scott 's work

Note Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)

Remember that the Commutative Property establishes "The order of the addends does not alter its result"

so

(24+16)=(16+24)

A = (1/2)(24 + 16)(8)=160 cm²

Verify Tara's work

Note Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)

A = (1/2)(16+24)(8)=160 cm²

[tex]\bf \begin{array}{|lllllllll|ll} \cline{1-9} label&A&B&C&D&E&F&G&H\\ &&&&&&&&&\\ pennies&2^0&2^1&2^2&2^3&2^4&2^5&2^6&2^7\implies 128\\ \cline{1-9} \end{array}[/tex]

Answer: part 2: 2n-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

You could use the 'brute force' method, which would be to simply write out all the possible subsets.  We could avoid repetition within the subsets.

{2} would be the first subset; it contains one even number.

Next would be {2, 4}, next {2, 4, 6} ... {2, 4, 6, ... 94, 96, 98, 100}.  Provided that we correctly understand what this problem is asking for, writing out and then counting all these subsets should answer the question.

Answer:

answer is Z

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

This is a skewed distribution so the best measure of centre is the median.

The best measure of spread  is the IQR because of the skewed distribution.

Answer:

1/2

Step-by-step explanation:

A die has 6 sides, in which 3 numbers (2 , 4 , 6) are even.

Simplify: 3/6 = 1/2

There is a 1/2 chance that blue is even and green is even.

~

Answer:

x= 25, y = 19

Step-by-step explanation:

Solve the following system:

{x = y + 6 | (equation 1)

9 y - 8 x = -29 | (equation 2)

Express the system in standard form:

{x - y = 6 | (equation 1)

-(8 x) + 9 y = -29 | (equation 2)

Swap equation 1 with equation 2:

{-(8 x) + 9 y = -29 | (equation 1)

x - y = 6 | (equation 2)

Add 1/8 × (equation 1) to equation 2:

{-(8 x) + 9 y = -29 | (equation 1)

0 x+y/8 = 19/8 | (equation 2)

Multiply equation 2 by 8:

{-(8 x) + 9 y = -29 | (equation 1)

0 x+y = 19 | (equation 2)

Subtract 9 × (equation 2) from equation 1:

{-(8 x)+0 y = -200 | (equation 1)

0 x+y = 19 | (equation 2)

Divide equation 1 by -8:

{x+0 y = 25 | (equation 1)

0 x+y = 19 | (equation 2)

Collect results:

Answer:  {x = 25 , y = 19

Answer: X= -29, Y= -267 over 10

Step-by-step explanation:

X= -29, substitute the value of X into the equation 6+y-8(-29)+9y an then solve for Y...

Hope this helps!

The expression '2 3/2' is a mixed number. Converting this to an improper fraction results in 7/2, which simplifies to 3.5. This does not match any of the provided options.

The expression '2 3/2' implies that we are dealing with mixed numbers, meaning you have a whole number and a fraction combined. When you see this, you should convert the mixed number into an improper fraction. The way to do this is to multiply the whole number by the denominator of the fraction and then add the numerator to this product. In this case that would be (2*2) + 3 which equals 7. Your new fraction would be 7/2 which equals 3.5 when simplified to a decimal. This does not correspond to any of the provided options (A, B, C, D), signifying that the original question may have been misinterpreted or contains a typographical error.

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2 3/2 is equal to 7/2 or D) Two times the square root of 16​.

When we have a whole number followed by a fraction, we can convert it to an improper fraction.

To do this, we multiply the whole number by the denominator of the fraction and add the numerator.

So in this case, 2 x 2 + 3 = 7.

Therefore, 2 3/2 is equal to 7/2 or D) Two times the square root of 16​.

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14×3×3=126. So 126 is your answer.

Answer:

14*4*3         168

Step-by-step explanat