Use back substitution to solve this problem

Answer:

t=r/d; t=0.2

Step-by-step explanation:

If d=r/t, then multiple both sides by t, to get td=r, then divide both sides by d, to get t=r/d. So t=8/40 t=0.2

Answer:

  H = M/(2A +2T)

Step-by-step explanation:

Factor out H and divide by its coefficient.

  M = 2HA +2HT

  M = H(2A +2T)

  M/(2A +2T) = H

  H = M/(2A +2T)

Answer:

5.75

Step-by-step explanation:

11.25 - 5.5 = 5.75.

So, Ana must take 5.5 more mL of Medicine A than Medicine B.

Hope this helps!

Answer:

-1/8

Step-by-step explanation:

[tex](-2)^-3 \\=\frac{-1}{2}^{3}\\=\frac{-1}{8}[/tex]

Answer:

-1/8

Step-by-step explanation:

[tex]\left(-2\right)^{-3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\\left(-2\right)^{-3}=\frac{1}{\left(-2\right)^3}\\\\=\frac{1}{\left(-2\right)^3}\\\\\left(-2\right)^3=-8\\\\=\frac{1}{-8}\\\\=-\frac{1}{8} \\\\\left(\mathrm{Decimal:\quad }\:-0.125\right)[/tex]

Answer:

The answer is B. sin A = 0.5

Step-by-step explanation:

Answer:

[tex](x+4,y-5)[/tex]

Step-by-step explanation:

Studying the figures ABCD and A'B'C'D', we can look at just one point and figure out the transformation from that.

Point A is at (-7, 8)

Point A' is at (-3, 3)

If we look at the x values, -7 and -3, we can see that the value changed by 4. So [tex]x+4[/tex] will be what the x becomes.

Also looking at the y values, we can see that the values were 8 and 3 - that's a change of -5, so our y is [tex]y-5[/tex].

Combining these, we get [tex](x+4, y-5)[/tex].

Hope this helped!

Answer: A.  (x,y) → ( x+4,y-5)

Step-by-step explanation:

This a rigid transformation and is being translated to find the transformation you could use any vertex.

Using the image of B  and to get  to B prime we have to move  4 units to the right and 5 units down.

So we could describe the whole transformation as (x,y) → ( x+4,x-5)

Answer:

a + s = 394     total tickets sold is 394 s = a - 56       56 fewer student tickets than adult substitute a-56 in place of s in 1st equation and solve for a a + (a - 56) = 394 2a - 56 = 394 2a = 450 a = 225 adult tickets sold s = a-56 = 169 student tickets sold

Hoped I helped

Answer:

1/46 is already in the simplest form.

Answer:

1/46 is already in its simplest form.

Answer:

59.96

Step-by-step explanation:

when 67% if 89.5 is expressed in numbers,

[tex]\frac{67}{100}*89.5\\ \frac{5996.5}{100}\\ =59.96[/tex]

Answer:

multiplication

Step-by-step explanation:

it seems the best

Answer:

x = 6

Step-by-step explanation:

Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.

Therefore, PQ = QR. Which is:

[tex] 3x + 14 = 7x - 10 [/tex]

Solve for x. Collect like terms

[tex] 3x -7x = - 14 - 10 [/tex]

[tex] -4x = -24 [/tex]

Divide both sides by -4x

[tex] x = 6 [/tex]

Answer:

9% of $1500 is $15 so she gains an extra $15 for each of the 18 years

$1500 in the bank each year for 18 years is $27000 after 18 years

$15 each year as well so that’s an extra $270 in the bank

The total in the bank is the sum of what she has invested and the interest so the total in the bank is $27270

Step-by-step explanation:

By Thales' theorem:

[tex]\[\begin{array}{l}\frac{{18}}{{2x + 2}} = \frac{{24}}{{3x + 1}}\\18(3x + 1) = 24(2x + 2)\\54x + 18 = 48x + 48\\6x = 30\\x = 5\\A.\end{array}\][/tex]

Answer:

eds bageles are $.22 per bagel and best bagels are $.23 per bagel.

Step-by-step explanation:

Answer:

  60°

Step-by-step explanation:

The definition of cosine tells you ...

  cos(β) = 3/6 = 1/2

  β = arccos(1/2) . . . . use the inverse cosine function to find the angle

  β = 60°

_____

The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...

  1 : √3 : 2

The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.

Answer: P, T, Y

This is because the points on the line are straight

Option - A is the correct answer.

We have a geometrical figure given in the question.

We have to determine which set of points are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

According to question -

It can be seen that only one set of points - (P, T, Y) lie on the same straight line. Of the options mentioned, one is - (P, T, Y)

Hence, the correct option is Option - A.

To solve more questions on Collinear points, visit the link below -

brainly.com/question/13069924

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Answer:

7/4 = 1.75

Step-by-step explanation:

step 1: pick two points on the line that have nice integer coordinates.

--> (3,4) and (-1,-3)

step 2: calculate the y difference and the x difference

--> y difference: 4 - -3 = 7

    x difference: 3 - -1 = 4

step 3: the slope is y difference / x difference

--> slope = 7/4

Answer:

3/5^3

3/5^3 = 27

125

= 0.216

Step-by-step explanation:

Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e. for five-hundredths enter 5/100. If you are using mixed numbers be sure to leave a single space between the whole number and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.

Because slash is both signs for fraction line and division, we recommended use colon (:) as operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

Colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.

An asterisk * or × is the symbol for multiplication.

Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.

The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2

Calculator follows well-known rules for order of operations. Most common mnemonics for remembering this order of operations are:

PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction

BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.

GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.

Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

Answer:

[tex]\frac{536}{15}[/tex] or [tex]35\frac{11}{15}[/tex] (they're the same)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diagram is not given in this question, but we can proceed anyways.

from the problem statement we can observe that the radius of the arc is same as the width of the door

a. the radius is 4.2 cm

b. the length of the arc given that the central angle is 25°  can be gotten using the formula stated bellow

arc length = 2 π r *(∅/360)

substituting we have

arc length = 2*3.142*(225/360)

arc length= 6.284*0.625

arc length=3.92 cm

Answer:

200,000

Step-by-step explanation:

To solve this, you can divide the 2019 total projected employment (210,000) by 1 + the growth rate (.05) to find the 2009 total employment.

210,000 / (1 + .05) = 200,000

I hope this helps!

-TheBusinessMan

Answer:

[tex]y=-0.5x+4.5[/tex]

Step-by-step explanation:

The slope of [tex]y=2x-6[/tex] is:

The negative reciprocal of that slope is:

So the perpendicular line will have a slope of [tex]-1/2[/tex]:

And now put in the point [tex](1,5)[/tex]:

And that answer is OK, but let's also put it in [tex]y=mx+b[/tex] form:

Answer:

0

Step-by-step explanation:

16x2= 32 and 32x1=32 so 32-32=0

Answer:

[tex]\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }[/tex]

Step-by-step explanation:

Given equation is

[tex]x^2 + y^2 + 6x-8y - 25 = 0[/tex]

Adding 25 to both sides

[tex]x^2 + y^2 +6x-8y = 25[/tex]

Completing squares

[tex]x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25[/tex]

Both of their "b" is -3 and 4 respectively

So, adding (-3)² => 9 and (4)² => 16 to both sides

[tex](x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}[/tex]

Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex], where center = (h,k) and radius = r.

We get:

Center = (-3,4)

Radius = [tex]5\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

cosine is negative in 2nd and 3rd quadrant.

cotangent is negative in 2nd and 4th quadrant.

In the second quadrant, both cosine and cotangent are negative.

In the first quadrant all trig functions are positive, In the second quadrant sine and sec are positive in the third quadrant tan and cot are positive, and in the fourth quadrant cos and cosec are positive.

We know there are four quadrants in an XY plane.

We also know that sine is positive on 1st and second quadrants and cosine is positive on the first and fourth quadrants.

tan = (sin/cos).

So, cot = 1/tan = cos/sing.

∴ cotangent is negative if any one of sine and cosine is negative which is in the second and fourth quadrants because in the third quadrant both sine and cosine are negative making cotangent positive.

∴ In the second quadrant cosine and cotangent, both are negative.

learn more about trig functions here :

https://brainly.com/question/14361710

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Answer:

13°

Step-by-step explanation:

The smallest angle in a triangle is the angle opposite the shortest side.

In this case the angle opposite side 9

let the angle be x, then using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{40}[/tex] , thus

x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{40}[/tex] ) ≈ 13° ( to the nearest degree )

We have [tex]h(p)=p^2+2p[/tex] and [tex]h(p)=3[/tex] which means we can equate:

[tex]p^2+2p=3[/tex].

Subtract 3 from both sides:

[tex]p^2+2p-3=0[/tex].

Then solve for p:

[tex]p^2+2p-3=0[/tex].

[tex](p-1)(p+3)=0[/tex].

So the product of two factors (p-1) and (p+3) is 0 which means at least one of the factors must be 0:

[tex]p-1=0\implies p_1=1[/tex].

Or

[tex]p+3=0\implies p_2=-3[/tex].

Hope this helps.