A metalsmith is mixing two molten metals, each containing different percentages of silver. The table shows the amount of each molten metal used. Which two expressions are both equivalent to t, the total number of grams of silver in the mixture?
A: (15)(0.75) and 0.7(15 – x) + 0.9x
B: (15)(0.75) and 0.7(15 – x)(0.9x)
C: 15 + 0.75 and 0.7(15 – x) + 0.9x
D: 15 + 0.75 and 0.7(15 – x)(0.9x)

Answer:

see below

Step-by-step explanation:

Formula: Center Not at Origin:

New point = k( x-a) +a, k( y-b) +b  where k is the scale factor and ( a,b) is center of dilation

New point = -2( x-4) +4, k( y-6) +6  

The scale factor is k = -2

Taking the top point ( 1,9)

New point = -2( 1-4) +4, -2( 9-6) +6

                   = -2(-3) +4 , -2(3) +6

                       6+4, -6+6

                         10,0  

Taking the bottom left point ( 1,7)

New point = -2( 1-4) +4, -2( 7-6) +6

                   = -2(-3) +4 , -2(1) +6

                       6+4, -2+6

                         10,4  

Taking the bottom right point ( 2,7)

New point = -2( 2-4) +4, -2( 7-6) +6

                   = -2(-2) +4 , -2(1) +6

                       4+4, -2+6

                         8,4  

Answer:

so the value of x is 8.3333≈8.3

Step-by-step explanation:

3x:10=5:2

[tex]\frac{3x}{10}=\frac{5}{2}[/tex]

by cross-multiplication

3x×2=5×10

6x=50

6x/6=50/6

x=8.33

i hope this will help you :)

Answer:

The radius is the square root of the constant term, z

Step-by-step explanation:

makes sense, also took the test :)

Answer:

C. The radius is the square root of the constant term, z.

Step-by-step explanation:

Hope this helps :)

Answer: w might be 9

Step-by-step explanation: the length of each sides of the smallest shaped polygon is 3 times less( like 6 in the biggest shape, it is 2 in the smallest one= 6/3:2) x might be 12 . And in other ways we can say that each length of the biggest shaped polygon is 3× the length of the smallest one.

Answer:

solution,

The two polygons are same.

[tex] \frac{4}{x} = \frac{y}{15} = \frac{3}{w} = \frac{2}{6} = \frac{z}{4} [/tex]

[tex] \frac{3}{w} = \frac{2}{6} \\ or \: 2w = 3 \times 6( \: cross \: multiplication) \\ or \: 2w = 18 \\ or \: w = \frac{18}{2} \\ w = 9[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

All angles in a rectangle are congruent, because in a rectangle, all angles are 90 degrees.

Answer:

The answer is option C.

Step-by-step explanation:

[tex] \sqrt{ {81d}^{6} } = \sqrt{81} \times \sqrt{ {d}^{6} } \\ = 9 {d}^{3} [/tex]

Hope this helps you

Answer:c

Step-by-step explanation:

Answer:

[tex]\boxed{x = -6}[/tex]

Step-by-step explanation:

[tex]x-48 = 6(x-3)[/tex]

Resolving parenthesis

[tex]x - 48 = 6x-18[/tex]

Adding 18 to both sides

[tex]x-48+18 = 6x\\x-30 = 6x[/tex]

Subtracting x from both sides

[tex]-30 = 6x-x\\-30 = 5x[/tex]

Dividing both sides by 5

[tex]-30/5 = x[/tex]

[tex]-6 = x\\[/tex]

OR

x = -6

Answer:

Step-by-step explanation:

x - 48 = 6(x - 3)

Expand the terms in the bracket

That's

x - 48 = 6x - 18

Group the constants at the right side of the equation and the ones with variables at the left side

x - 6x = 48 - 18

- 5x = 30

Divide both sides by - 5

Hope this helps you

Answer:

x = 6

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, thus

6x - 15 = x + 15 ( subtract x from both sides )

5x - 15 = 15 ( add 15 to both sides )

5x = 30 ( divide both sides by 5 )

x = 6

Answer:

X=6 Read explination

Step-by-step explanation:

A parallelogram has the perrimeter of both opposite sides equal

So we know that

6x-15=x+15

This is because in a parrellelogram the opposite sides are equal  

so breaking it down

6x-15=x+15

(add 15 to both sides)

6x=x+30

(subtract x from both sides)

5x=30

(divide both sides by 5)

x=6

Answer:

12617.13

Step-by-step explanation:

250(1+0.103)^40= 12617.13

hope it help

Answer:

12617.13

Step-by-step explanation:

Answer:

Price of Bond X : $1,162.89

Price of bond Y : $854.66

Step-by-step explanation:

Given the following information :

Bond X :

Face value = $1000

Yield to maturity (YTM) / market interest rate = 9%

Coupon rate = 11%

Years to maturity = 15 years

Compounding frequency = semianually

Using the online bond price calculator, The bond price will be $1,162.89. The bond is sold at premium, since the par value is lesser than the bond price.

For Bond Y:

Face value = $1000

Yield to maturity (YTM) / market interest rate = 11%

Coupon rate = 9%

Years to maturity = 15 years

Compounding frequency = semianually

Using the online bond price calculator, The bond price will be $854.66. The bond is sold at a discount , since the par value is greater than the bond price.

Answer:

4:7

Step-by-step explanation:

The number of students in the class is:

boys + girls

12 + 16 = 28

There are 28 students.

The ratio of girls to students is:

16:28

Simplify the ratio.

4:7

Answer:

4:7  

Step-by-step explanation:

I got it right on the test

Answer:

Step-by-step explanation:

Given sinx< cos x and 0°< x < 90°, to get the possible value of x, we need to solve the given inequality for x.

sinx< cos x

Dividing both sides by cos x

sin x/cos x < cos x/cos x

tan x < 1

x < [tex]tan^{-1}1[/tex]

x < 45°

Since x is less than 45°, then one of the possible value of x can be 30° since 30° is less than 45° and 30° falls within the given range of values.

Answer:

28.

Step-by-step explanation:

I just did the question and I got it right. The answer above is right. The image below is where I did the question and has the picture attached next to it too.

*And I accidentally clicked the one star option, that's why it has such a low score.

An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.

The value of y is 28.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.

m∠CAB = 34

m∠CBA = x - 5

m∠ACB = 4y

Triangle ABC is an isosceles triangle.

AC and BC are sides are equal.

This means,

m∠CAB = m∠CBA

34 = x - 5

34 + 5 = x

x = 39

Now,

The sum of the angles in a triangle is 180 degrees.

This means,

34 + (x -5) + 4y = 180

34 + (39 - 5) + 4y = 180

34 + 34 + 4y = 180

68 + 4y = 180

4y = 180 - 68

y = 112 / 4

y = 28

We can cross-check.

34 + 34 + 4 x 28 = 180

34 + 34 + 112 = 180

180 = 180

Thus,

The value of y is 28.

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Answer: a) 26

Step-by-step explanation:

-a would be because as you can see there is a pattern of sticks, so what i did was count up the sticks and i found that there was 6 in the first one. So i counted the second one and it was 10 so i realized that all i had to do was add 4.

and for b i think when it says n it means the nth term which is 4 so i think it means pattern 4 which would be 18 so try that out

hope this helped x

Answer: b, c, and e

Step-by-step explanation:

I hope I helped

The standard form of the equation of straight line is given by

y - 1 = -1/6(x + 4)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have a table as given in the image attached at the end of answer.

The slope of the line will be -

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 2)/(- 4 + 10)

m = - 1/6

The standard form of the equation of straight line is given by -

y - y₂ = m(x - x₂)

y - 1 = -1/6(x + 4)

Therefore, the standard form of the equation of straight line is given by

y - 1 = -1/6(x + 4)

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[Refer to the image attached for complete question]

Answer:

Step-by-step explanation:

Compound Interest Formula, Amount, [tex]A(n)=P(1+r)^n[/tex]

Interest=Amount - Principal

[tex]I=P(1+r)^n-P[/tex]

At the end of 1 year, interest =Rs450, therefore:

[tex]450=P(1+r)-P\\450=P+Pr-P\\450=Pr[/tex]

At the end of 2 years, interest =Rs945, therefore:

[tex]945=P(1+r)^2-P\\945=P(1+r)(1+r)-P\\945=P(1+r+r+r^2)-P\\945=P(1+2r+r^2)-P\\945=P+2Pr+Pr^2-P\\945=2Pr+Pr^2[/tex]

Recall: Pr=450

Therefore:

[tex]945=2(450)+Pr^2\\945-900=Pr^2\\Pr^2=45[/tex]

Comparing Pr=450 and [tex]Pr^2=45[/tex]

[tex]\dfrac{Pr^2}{Pr}= \dfrac{45}{450}\\r=0.1[/tex]

Substitute r=0.1 to obtain P

0.1P=450

P=Rs4500

Therefore:

Answer:

270[tex]\sqrt{3}[/tex] cm³

Step-by-step explanation:

A regular hexagon can be cut into 6 equilateral triangles.

The area (A) of an equilateral triangle can be calculated as

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ← where s is the side length, here s = 6

A = [tex]\frac{6^2\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] cm² ← multiply by 6

area of base = 6 × 9[tex]\sqrt{3}[/tex] = 54[tex]\sqrt{3}[/tex] cm²

The volume (V) of the prism is calculated as

V = area of base × height = 54[tex]\sqrt{3}[/tex] × 5 = 270[tex]\sqrt{3}[/tex] cm³

Between 6 and 7

6×6=36

7×7=49

hopefully this helped

The number √37 is lies between whole numbers 6 and 7.

We have to given,

A number is, √37

By the definition of square root, we get;

⇒ √37 = 6.08

And, We know that,

Number 6.08 is lies between whole number 6 and 7.

Hence, We get;

⇒ 6 < √37 < 7

Therefore, The number √37 is lies between whole numbers 6 and 7.

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Answer:

(12, 40)

Step-by-step explanation:

The first thing is to assume that we have a point with the following coordinates (x, y).

Now, we can have two different cases since the meaning of the expansion of a point is moving to a new point that is a greater distance from the origin if we are expanding by a value, that is, an integer in the system of coordinates and the other case is that if we are dilating by a fraction that is between 0 <x <1, then the distance from the origin decreases.

Now, the point (x, y) goes through an expansion by a scale factor f (with the origin as the expansion point), then the new coordinate of the point = [f * x, f * y], that scale factor has the value of 3, so if we replace we have:

(3 * 4, 4 * 10) = (12, 40)

Answer:

a). [tex]V=\frac{U.F}{U-F}[/tex]

b). V = 15 units

Step-by-step explanation:

Focal length F of a lens made by combining two lenses of different focal lengths U and V will be,

[tex]\frac{1}{F}=\frac{1}{U}+\frac{1}{V}[/tex]

A). By solving the given formula,

    [tex]\frac{1}{V}=\frac{1}{F}-\frac{1}{U}[/tex]

    [tex]\frac{1}{V}=\frac{U-F}{U.F}[/tex]

    [tex]V=\frac{U.F}{U-F}[/tex]

B). If F = 6 and U = 10 then we have to find the value of V.

    By substituting the given values in the formula,

    [tex]V=\frac{6\times 10}{10-6}[/tex]

    [tex]V=\frac{60}{4}[/tex]

    V = 15 units

    Therefore, focal length (V) of the lens = 15 units

Answer:

c = 21

Step-by-step explanation:

c + 2c + 12 = 75

Combine like terms.

3c + 12 = 75

Subtract 12 from both sides.

3c = 63

Divide 3 on both sides.

c = 21

Answer:

B

Step-by-step explanation:

The area of the square can be calculated using S^2 = x^2

The area of the circle is pi * r^2

= 22/7 * (x-1)^2

= 22(x-1)^2/7

So we need the value of x, that will make;

x^2 = 22(x-1)^2/7

In this kind of scenario, since we have options, it is best to test values instead of going through long calculations

Let’s try 2.29

So;

2.29^2 = 22/7(2.29-1)^2

5.2441 = 5.23

So close , but let’s see if any other value will

give us a closer value

Let’s work with 1.66

1.66^2 = 22/7(1.66-1)^2

2.7556 = 1.369

This is far from what we need

Let’s try 0.5

0.5^2 = 22/7(0.5-1)^2

Thus gives a negative answer on the right hand side, so no need trying

And lastly 1.25

1.25^2 = 22/7(1.25-1)^2

1.5625 = 0.1946

So the first test still gives the most probable answer to a decimal place accuracy

Answer:

b. 2.29

Step-by-step explanation:

the answer above is correct please give them the brainiest  

Answer:

y=2(x+2)(x+3)

Step-by-step explanation:

First, we need to factor the right side:

y=2(x^2+5x+6)

Now, we can have an incomplete equation like this:

y=2(x+_)(x+_)

In the blanks, we need to fill out numbers that add to be 5 and multiply to be 6. What are factors of 6? 6 and 1, 2 and 3. Do 6 and 1 add to be 5? No. Do 2 and 3 add to be 5? Yes!

So, our factored form is

y=2(x+2)(x+3)

Answer: Hold on

Step-by-step explanation: LEt me see this is tricky

Answer: P= 2,800, r= 0.035, n= 12, t= 0.75

Step-by-step explanation:

I guessed and got it right!

Step-by-step explanation:

taking common (a-b)

so we get the answer

Answer:

q = -7

Step-by-step explanation:

3 ^ -q * 1/27 = 81

Rewriting each as a power of 3

3 ^ -q *  3^ -3 = 3 ^4

We know that a^b * a^ c = a^ ( b+c)

3 ^ (-q -3) = 3 ^4

The bases are the same so the exponents are the same

-q-3 = 4

Add 3 to each side

-q-3+3 = 4+3

-q =7

Divide by -1

q = -7

Answer:

sin = 12/13 and tan = 12/5

The value of sin α will be 12/13 and tan α  will be 12/5 for the given triangle such that cosα= 5/13.

Trigonometric functions are functions for right angle triangle which gives the relation between the angle and sides of the triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

The trigonometric functions are found in the four quadrants, as well as their graphs, domains, and differentiation and integration.

We know that

sin²α  + cos²α  =1  ⇒ sin²α  = 1 - cos²α

Given that cosα = 5/13 so by putting it

sin²α  = 1 - (5/13)²

sin²α  = 144/169  ⇒ sinα = 12/13.

Now since tanα = sinα /cosα  

tanα  = (12/13) ÷ ( 5/13)

tanα = 12/5.

Hence the value of sinα will be 12/13 and tanα will be 12/5.

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Answer:

It makes 360 / 60 = 6 revolutions per second. 6 revolutions is 12π radians.