A lorry travels at a speed of 45 km/h for 2 hours from factory P to factory Q. Then the lorry takes 30 minutes more for its return journey. Calculate the average speed.​

The measures of the angles are given as follows:

1. p = 67º.

2. q = 27º.

To solve item 1, first we have to consider that the sum of the internal angles of a triangle is of 180º, hence we find angle x, which is the interval angle of angle p.

Hence:

x + 35 + 32 = 180

x + 67 = 180

x = 113º.

An angle and it's respective external angle are supplementary, meaning that the sum of it's measures are of 180º, hence:

p + x = 180

p + 113 = 180

p = 67º.

The internal angles are given as follows:

The sum of their measures is of 180º, hence we can simply solve for q as follows:

q + 128 + 25 = 180

q + 153 = 180

q = 27º.

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Answer:

The measures of the angles are given as follows:

1. p = 67º.

2. q = 27º.

Step-by-step explanation:

But you didn't have to cut me off

Make out like it never happened and that we were nothing (aah-ooh)

And I don't even need your love (ooh)

But you treat me like a stranger, and that feels so rough (aah)

No, you didn't have to stoop so low (ooh)

Have your friends collect your records and then change your number (aah)

I guess that I don't need that, though

Now you're just somebody that I used to know

According to the solving the space between Arthur and Jamie are 39.1 meters.

A coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

The length of the line segment bridging two locations in a plane is known as the distance between them. d=√((x2 – x1)² + (y2 – y1)²).  is a typical formula for determining the separation between two places. Any two sites on an x-y plane or coordinate plane can have their distance between them calculated using this equation.

location of Arthur is (20, 30)

location of Jamie is (45, 60)

Let's apply the rule of distance to determine how far away they are because we know that :

d = √((X₂ - X₁)² + (Y₂ - Y₁)²)

let substituting the value we get:

d = √((X₂ - X₁)² + (Y₂ - Y₁)²)

d = √((45 - 20)² + (60 - 30)²)

=   √(25)² + (30)²)

= 39.1

According to the solving the space between Arthur and Jamie are 39.1 meters.

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It takes Phindi to run almost 22 tracks to cover 12kms

Given that,

First you have to figure out the length of the track whihc is circumference of circle ,

r is the radius  of circular track which is 88m

The athlete has to run 12km on the track

Circumference of circle = 2πr

Solving circumference will give length of the circular track which is,

Circumference of circle = 2(3.14)(88)

                                          =552.6 meters

If she covers 552.6 m whe runs one circular track then,

1 circular track -------- 552.6 meters

? circular track -------- 12000 meters or 12 kilometers

No of circular tracks = 12000/552.6 = 21.7 tracks

Therefore, It takes Phindi to run almost 22 tracks to cover 12kms

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The equation of the line passing through P(0, 0) perpendicular to y = -9x - 1 will be  [tex]y = \frac{1}{9}x[/tex]

The given question states that the line passes through the point P(0, 0) perpendicular to the line y = -9x - 1. We have to find out the equation of the line. We have to find the equation in slope-intercept form.

We know the slope intercept is: y = mx + b

Also, given the perpendicular line has slope m₂ = -9 according to slope-intercept form. And we know that perpendicular lines have a slope that is equal to the negative reciprocal.

So, the Slope of the line m₁ = Negative reciprocal of the slope of the perpendicular line.

=>  [tex]m_{1} = -\frac{1}{m_{2} }[/tex]

=> [tex]m_{1} = -\frac{1}{(-9)}[/tex]

=> [tex]m_{1} = \frac{1}{9 }[/tex]

We get the slope [tex]m_{1} = \frac{1}{9 }[/tex]. Also, it is given that the line passes through (0, 0) so the y-intercept b = 0. Putting these values in slope-intercept form, we get:

=> y = mx + b

=> [tex]y = \frac{1}{9} x[/tex]

Hence, the equation of the line is [tex]y = \frac{1}{9} x[/tex]

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A segment that is both an altitude and a median of a triangle is a perpendicular bisector.

A median is a segment from a vertex to the midpoint of the opposite side. There are of course three medians of a triangle; they’re concurrent, meeting at a point called the centroid.

An altitude is a segment through a vertex that’s perpendicular to the opposite side; the foot of the altitude (at the point of perpendicularity) either on the side or on the line resulting from extending the side. The three altitudes of a triangle are also concurrent, meeting at a point called the orthocenter.

And when both the altitude and a median of a triangle are the same, then it is called a perpendicular bisector.

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Answer:

  -8k -2

Step-by-step explanation:

You want the simplified form of -2(k+1)-6k.

The process of simplifying an algebraic expression includes ...

Parentheses are removed using the distributive property. The factor outside parentheses multiplies each term inside.

  -2(k +1) -6k

  = (-2)(k) +(-2)(1) -6k = -2k -2 -6k

Terms with the same variable content can be combined by adding their coefficients. (The distributive property is involved here, too.)

  = (-2 -6)k -2 = -8k -2

The simplified expression is -8k -2.

The distance that member of the cross country team ran is 6.2 miles yesterday.

Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage.

The cross-country team ran 1.772 hours yesterday, today they ran 1.49 hours Each member of the team ran 3.5 miles every hour.

The number of miles attained by each member of the team yesterday can be calculated as follows:

3.5 × 1.772= 6.2

Hence for yesterday each member of the team ran for 6.2 miles.

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Find out the total number of animals

25+12=37 animals

Compare the number of birds to the total number of animals

number of birds=25

so

25/37

or

25:37

or

25 to 37

SOLUTION

Line 1 is given as

let's find the equation of line 2, it passes through points (2, 3) and (4, 4)

The slope is

The slope of line 2 is 1/2

If the two lines are perpendicular, then the product of their slope will be = -1, that is

Since the product of their slope = -1

Hence Line 1 and Line 2 are perpendicular

Anwser is 18

I used a website

Answer: x = 18

Isolating a variable: rearranging the equation to make the variable on side of the equation and the others on the other side

1. Collect like terms

2. Inverse operations to isolate

3. simplify if necessary

Calculations:

[tex]3x -14 +3x +9= 103[/tex]

Collect like terms: [tex]6x -5 =103[/tex]

Inverse operations:

[tex]6x = 103 +5[/tex]

[tex]6x= 108[/tex]

[tex]\frac{6x}{6}=\frac{108}{6}[/tex]

∴ [tex]x= 18[/tex]

The probability of drawing a consonant from the given set of cards is 0.66.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The given letters are  M, A, T, H, I, S, F, U and N.

Total number of letters are 9.

The number of vowels is 3.

Then, the number of consonants is 9 - 3 =6.

Now, the probability for choosing consonant is given as follows,

P(Consonant) = Number of Consonants ÷ Total letters

⇒ 6/9 = 0.66

Hence,  the probability of randomly drawing a consonant is given as 0.66.

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Answer: 6/10 is answer

Step-by-step explanation:

Just trust please

we are given m=6 and a point MEANING WE CAN SUBSTITUTE THE KNOWNS TO GET C IN THE EQUATION Y=MX+C

[tex]2 = 6( \frac{1}{2} ) + c \\ 2 = 3 + c \\ c = 2 - 3 \\ c = - 1[/tex]

THEREFORE

[tex]y = 6x - 1[/tex]

IS THE ANSWER.

HOPE THIS HELPS

Answer: 6

Step-by-step explanation: .

Answer:

x=12.92

cube root of 9 Is 2.08 so you minus 15-2.08=12.92

If the bricklayers lay 5% more blocks each day. The function is exponential  and discrete.

An exponential function is a function that increases or decreases at an increasing rate. It does not increase by a constant number.

The form of an  exponential function: [tex]e^{x}[/tex]

Where:

• x = the variable

• e = constant

For example, the blocks layed on the first day is 100.

A discrete variable is a variable that assumes only a finite number of values. A discrete variable can be counted.

A linear function is a function that increases at a constant rate. For example, if the bricklayers lay 100 bricks every day, it can be modelled as a linear function.

A continous variable does not take on a finite number of values. It cannot be counted and it is instead measured.

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Assuming the question is : How much does x liters/milimeters of oil weigh?

First, we calculate how much mass did the bottle of oil lose : 590 - 400 = 190 (grams)

Since it loses 190 grams after Sophia uses 200 milimeters of oil, 200 milimeters of oil weighs 190 grams (yes.)

-> 1 milimeter of oil weighs : 190/200 = 0.95(grams)

So, to calculate the mass of x *liters* of oil, we take 0,95 x 1000 times x.

For example : To calculate the mass of 22,5 liters of oil, we take 0,95 x 1000 x 22,5 = 21375 (g) or 21.35(kg).

always substitute the function

(for example here we have) h(x) with its value

goodluck :)

Hello!

Since h(x) = -3x + 2  and h(x) = -4

 [tex]\hookrightarrow \text{Thus: } -3x + 2 = -4[/tex]

Let's solve:

 [tex]-3x + 2 = -4\\-3x = -4-2\\-3x=-6\\x = 2[/tex]

Hope that helps!

The equation is 10x=2x+60

 x=15/2

∠CFH=75

∠CBD= 75

We are dealing with parallel lines, which are the lines that are equidistant to each other and never meet,  will never meet, when such lines are crossed by another line called the transversal creates many angles such as corresponding angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive angles.

Since, angle CBD and angle CFH are the corresponding angles and they are equal to each other, we are given CBD=2x+60 and CFH = 10x

therefore , 10x=2x+60

=>10x-2x=60

=>8x=60

x=15/2

So, the angle CBD= 2x+60= 2(15/2)+60=  75

and the angle CFH = 10x= 10(15/2)= 75

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i hope that this helps :)

The number of the people did we survey = 12/19

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers.

The set of whole numbers is 0 through 9 (inclusive). Every value in this set is an example of a whole number. Examples are 0, 15, 53, and so forth.

To convey a thorough grasp of more complicated number identifiers like real, rational, and irrational numbers, whole numbers are employed as building blocks. Calculations can be made simpler and issues can be resolved more quickly by rounding decimal numbers to the next whole number.

According to question,

the exact percentage of the people is between 24% and 38%

24%÷ 38%

=0.24/0.38

=12/19

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After doing some mathematical operations we can conclude that there are 11 servings in a fruit can.

So, servings in a fruit can:

Now, solve the following as follows:

Therefore, after doing some mathematical operations we can conclude that there are 11 servings in a fruit can.

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The most appropriate choice for  linear equation will be given by -

8x - (x - 35) = 2x - (7 + x) is the required equation with x = -7

What is  linear equation?

At first it is important to know about algebraic expression

Algebraic expression consist of numbers and variables connected with addition, subtraction, multiplication and division.

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let y be filled in the gap

8x - (x -35) = 2x - (y + x)

8x - x + 35 = 2x - y - x

7x + 35 = x - y

putting x = -7

7(-7) + 35 = -7 -y

y = -49+35 + 7

y = 7

8x - (x - 35) = 2x - (7 + x) is the required equation with x = -7

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××1=× 123 =×/1= the value of x is one

Answer:

v = -1.5

Step-by-step explanation:

[tex]v = 2 + ( -7 \times .5) = - 1.5[/tex]

Volume of the sphere = 17157.28 cubic centimeters

How to calculate the volume of a sphere?

Given:

Diameter (d) = 32

r = d/2 = 16

We know that the  volume of a sphere is,

[tex]V=\frac{4}{3} \pi r^{3} \\\\ = \frac{4}{3} (3.14) (16)^{3}\\\\=17157.28 cm^{3}[/tex]

What is the volume of a sphere?

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[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ d\ to\ r\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Calculating\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]

1. The slope is -2.

2. The slope is 1.

3. cost of 1 yards fabric is $6.49.

4. The average speed is 65 miles/ h.            

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

The slope of line is the measure of steepness or the direction of line the coordinate plane.

m = Δy/Δx

where, m is the slope

1. The co- ordinates of the graph is (0, 0) and (-1, 2)

slope = (2-0) / (-1 - 0) = 2/ (-1) = -2

Thus, the slope is -2.

2. The co-ordinates of the graph is (0, 0) and (4, 4)

slope = (4 - 0) / (4- 0) = 4/4  = 1

Thus, the slope is 1.

3. cost of 7 yards fabric = $45. 43

cost of 1 yards fabric = 45. 43/7

                                  = $6.49

4. Distance = 325 miles

Time = 5 hours

So, average speed = 325 / 5

                                = 65 miles/ h

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Answer: Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x < 7/2

Step-by-step explanation: graph included in link

The graph which shows the solution of the inequality 4x + 2 < 2x + 9 is the graph B.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

The given linear in equality is,

4x + 2 < 2x + 9

Find the solution set of the inequality.

Operate the like terms together.

Subtracting both sides by 2x,

2x + 2 < 9

Subtracting both sides by 2,

2x < 7

Dividing both sides by 2,

x < 3.5

Hence the correct graph is B.

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The missing values in the first month of payment in the amortization schedule are:

An amortization schedule is a table that shows the loan amount, the periodic payment, the portion of the regular payment that is the interest and the principal repayment, and the remaining balance after each period.

The amortization schedule presents the above information in an easy format for ready evaluation.

Auto Loan = $12,000

Annual interest rate = 3% compounded monthly

Loan period = 60 months (5 years x 12)

Monthly Payment = $287

Interest = $30 ($12,000 x 3% x 1/12)

Principal Repayment = $257 ($287 - $30)

Remaining Balance = $11,743 ($12,000 - $257)

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