A result of a number, what decreased by 15% equal 161. Find that number.

Answer:

  x = 11/9

Step-by-step explanation:

Eliminate parentheses, add 16x, subtract 21.

  7(3 -x) = 8(4 -2x) . . . . given

  21 -7x = 32 -16x . . . . . eliminate parentheses using the distributive property

  9x +21 = 32 . . . . . . . . add 16x

  9x = 11 . . . . . . . . . . . . subtract 21

  x = 11/9 . . . . . . . . . . . .divide by the coefficient of x

Answer:

a = 56.3°

Step-by-step explanation:

tan(a) = 9/6 = 1.5

atan(1.5) = 56.31°

Answer:

[tex]\boxed {\boxed {\sf 56.3 \textdegree}}[/tex]

Step-by-step explanation:

We are asked to find the measure of angle a.

This triangle is a right triangle because of the small triangle in the corner representing a 90 degree or right angle. Therefore, we can use trigonometric functions. The three main functions are:

The side measuring 6 is adjacent or next to angle a. The side measuring 9 is opposite angle a. Therefore, we will use the tangent function.

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

[tex]tan \ a = \frac{ 9}{6}[/tex]

Since we are solving for an angle measure, we use the inverse trigonometric function.

[tex]tan ^{-1} * tan \ a = tan ^{-1} * \frac{9}6}[/tex]

[tex]a= tan ^{-1} * \frac{9}6}[/tex]

[tex]a= 56.30993247[/tex]

Round to the nearest tenth. The 0 in the hundredth place tells us to leave the 3 in the tenth place.

[tex]a \approx 56.3[/tex]

The measure of angle a is approximately 56.3 degrees.

Answer:

Step-by-step explanation:

a:b = 3:2    ⇒   a = 3x  and  b = 2x

a - b = 5

3x - 2x = 5

x = 5

a = 3•5 = 15

b = 2•5 = 10

Answer:

About 13 weeks

Step-by-step explanation:

Answer:

The price in dollars per gallon is 8.4

Step-by-step explanation:

The ratio is a comparison between two quantities that is made using a quotient. In other words, a ratio is a comparison between two or more quantities that can be expressed as a fraction. If the quantities to be compared are a and b, the ratio between them is written as: [tex]\frac{a}{b}[/tex]

You know that the price in England is 1.4 pounds per liter and the current exchange rate is 1 pound = 1.65 dollars. So, being the following reasons:

and being the conversion factor 1 L = 0.26 gal expressed as a ratio:

you can see that the expression to find the equivalent price in dollars per gallon is:

[tex]\frac{1.4 pounds}{1 liter}*\frac{1.56 dollars}{1 pound}*\frac{1 liter}{0.26 gal}[/tex]

Taking into account that all unwanted units of measure are canceled and solving:

[tex]\frac{1.4 pounds}{1 liter}*\frac{1.56 dollars}{1 pound}*\frac{1 liter}{0.26 gal}=\frac{2.184 dollars}{0.26gal}= 8.4 \frac{dollars}{gal}[/tex]

The price in dollars per gallon is 8.4

Answer:

15/40

Step-by-step explanation:

[tex]0.375 = \frac{375}{1000} \\ \\ = \frac{15}{40} [/tex]

Answer:

53 1/3 km/h

Step-by-step explanation:

average speed = (total distance)/(total time)

average speed = distance/time

time * average speed = distance

time = distance/(average speed)

250 km at 75 km/h

distance = 250 km

time = (250 km)/(75 km/h) = 3.33333... hours

350 km at 70 km/h

distance = 350 km

time = (350 km)/(70 km/h) = 5 hours

200 km at 30 km/h

distance = 200 km

time = (200 km)/(30 km/h) = 6.6666...  hour

total distance = 250 km + 350 km + 200 km = 800 km

total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours

average speed = (total distance)/(total time)

average speed = (800 km)/(15 hours)

average speed = 53 1/3 km/h

The average speed of whole journey of the train is 45 km/hr

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Given that a train travels 250 km with a average speed of 75 km/hr, hence:

75 = 250/time

time = 3.33 hours

It the travel 200 km with average speed of 30km/hr, hence:

30 = 200/time

time = 6.67 hours

The total distance = 200 km + 250 km = 450 km

The total time = 3.33 hr + 6.67 hr = 10 hours

Average speed = total distance/total time = 450 km/10 hours = 45 km/hr

The average speed of whole journey of the train is 45 km/hr

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Answer:

3

3+3=6

3+3+5=11

13

13-3=10

10-3=7

15

15-7=8

8-5=3

32+43=75

75-40(highest ten)=35

76+15=91

91-70=21

Step-by-step explanation:

Hi there!

The given equation is:

y = -2x + 5………………(i)

Comparing the equation with y = mx+c, we get;

m1 = -2

Also another equation of the line which passes through point (-4,2), we get;

(y-2) = m2(X+4)............(ii) { using the formula (y-y1) = m2(x-x2)}

According to the question, they are perpendicular to eachother, So according to the condition of perpendicular lines;

m1*m2 = -1

-2*m2 = -1

or, m2 = 1/2.

Therefore, m2= 1/2.

Now, keeping the value of m2 in equation (ii).

(y-2) = 1/2(x+4)

y = (1/2)x + 4

Therefore, the required equation is: y = (1/2)x + 4.

Hope it helps!

Answer:

Upper Right

Step-by-step explanation:

All of them have different dips, therefore the one facing in a different direction must be the odd one out.

Answer:

top right graph

Step-by-step explanation:

3 of the 4 graphs start at negative infinity for negative x, and approach infinity as x approaches infinity.

The top right graph starts at infinity for negative x and approaches negative infinity as x approaches infinity.

Answer: top right graph

Answer:

D: {x∈R | -2 ≤ x ≤ 2 }

R: {y∈R | 0 ≤ y ≤ 4 }

Step-by-step explanation:

The domain ranges between -2 and 2

The range ranges between 0 and 4

Answer:

third option

Step-by-step explanation:

Given

f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

solve x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

The vertical asymptotes are x = 1 and x = - 2

Answer:

Below

Step-by-step explanation:

● 2x(7a+8a) -5+56×2÷3

● 14ax + 8a -5 +56×2÷3

When you have multiplication and division go from left to right

● 14ax + 8a -5 +112÷3

● 14ax + 8a -5 +112/3

● 14ax + 8a - 15/3 + 112/3

● 14ax + 8a + 97/3

Answer:

C. 0.10, because 6 of the 60 days were clear

Step-by-step explanation:

As per the question, you're in San Antonio which indicates 1st look in San Antonio's row.

Then we want the chance or probability it's clear, so look in clear column. We will find the value that is "6"

So 6 on a total of 60 which is the huge total. Accordingly,  Probability it is right, since that you are into the San Antonio. Then it becomes

[tex]= \frac{6}{60}[/tex]

= 0.1

Therefore the right answer is C.

Answer:

Step-by-step explanation:

Answer:

a) attached below

b) Ic3 = Ic2 + Ic1 + index of a fixed point in ( C°₁ U C°₂ )^c n c₃

Step-by-step explanation:

A) sketch of the arrangement of the cycles

attached below

b) prove that at least one fixed point in the attached region is bounded

Given that : Ic3 = Ic2 = Ic1 = 1

hence : Ic3 = Ic2 + Ic1 + index of a fixed point in ( C°₁ U C°₂ )^c n c₃

This is a prove that at least one fixed point is bounded by C1 , C2 , C3

Answer:

VW=6

Step-by-step explanation:

UW=VW+UV

5x=(5x-4)+(2x)

5x= 7x-4

7x-5x=4

2x=4

x=4/2=2

VW=5x-4=5(2)-4=10-4=6

I hope I helped you^_^

Let the cost of a lamp = x

6 lamps would cost 6x

He bought 3 lamps at 3x plus Thad 950 left.

3 lamps plus the 950

Would be the same amount as 6 lamps:

Set up an equation and solve for x:

3x + 950 = 6x

Subtract 3x from both sides:

950 = 3x

Divide both sides by 3:

X = 316.67

Each lamp was $316.67

Multiply the price of a lamp by 6:

316.67 x 6 = 1900

He had $1900

Answer: $1900

Step-by-step explanation:

Mr Lim had enough money to buy 6 similar lamps. However he only bought 3 such lamps. That means he had only spent half of his money (6-3=3).

So, if he take money remaining with him = x = $950

Amount of money he first had = 2x =$950×2 = $1900

Answer:

50%

Step-by-step explanation:

You take the 1500 shots and take away the 300 and 450 you get 750 you divide 750 from 1500 then you get 0.5 and you multiply it with 100 and you get the answer 50.

Out of 1500 flu injections the share of flu vaccines which has been given is 94.33%.

A percentage is that the number or ratio expressed as a fraction of 100. it's denoted by the expression %. it's calculated by the subsequent formula:

Percentage=Number/total*100

It is provided that out of 1500 flu vaccines , 300 got in September, 450 got in October and 665 got in November.

Total vaccines given= 300+450+665

=1415

Percentage=1415/1500*100

=0.9433*100

=94.33%

Hence the proportion of flue vaccine that has been given is 94.33%.

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#SPJ2

Answer:

Step-by-step explanation:

Vertically opposite angles are equal

x = 25°

Answer:

Your answer is correct

Step-by-step explanation:

SAS triangle is proven through b option.

Hope this helps....

Have a nice day!!!!

Answer:

Step-by-step explanation:7.12 meters tall

Answer:

72

Step-by-step explanation:

As you can see the top - view is a rectangle of 2 by 9 dimensions. Respectively the right - side view is a rectangle of 2 by 4 dimensions. The common dimension among both rectangles would be 2, making this rectangular prism have dimensions 2 by 4 by 9.

Therefore the rectangular prism will have a volume of 2 [tex]*[/tex] 4 [tex]*[/tex] 9

2 [tex]*[/tex] 4 [tex]*[/tex] 9 = 8( 9 ) = 72 cubic units

Solution : 72 unit cubes

Answer:

2/3

Step-by-step explanation:

the points are (2,-5) and (5,-3)

the slope is change in y over change in x

so the slope can be written as:

(-3-(-5))/(5-2)

thats 2/3

and thats the slope

:D hope this helps u

Answer:   1.4

Work Shown:

42 cupcakes : 30 minutes

42/30 cupcakes : 30/30 minutes

1.4 cupcakes : 1 minute

The unit rate is 1.4 cupcakes per minute. This assumes that the rate is kept the same.

Answer:

B, air pressure in a car tire.

Step-by-step explanation:

Discrete data is data which come in intervals, and isn't continuous.

The number of home runs can only go 0 -> 1 -> 2 -> 3, you can't have 2.5 or 3.2 home-runs.

The number of pills in a container can also only go 0 -> 1 -> 2. Again, can't have 0.7 pills.

The number of cars per household is also discrete. The number of cars in a household goes 0 -> 1 -> 2, you can't have half a car!

However, the air pressure is continuous. If you're increasing the air pressure, it'll (in theory) go from 0 -> 0.000...001 -> 0.000..002 etc. It doesn't "jump" from 0 pressure -> 1 pressure like the others, it goes smoothly. It can be any value.

So the air pressure isn't discrete data.

Answer:

x = 58

Step-by-step explanation:

The secant- tangent angle 51° is half the difference of the measures of the intercepted arcs, that is

[tex]\frac{1}{2}[/tex] (160 - x) = 51 ( multiply both sides by 2 )

160 - x = 102 ( subtract 102 from both sides )

58 - x = 0 , thus

x = 58

Answer:

I believe it is A. 1,1150.6cm^3

Step-by-step explanation:

To solve for the volume of a cone:

[tex]V = \pi radius^{2} \frac{height}{3}[/tex]