Solve this question using simultaneous equations.
To cover a distance of 10 km, Jacob runs some of the way at 15 km/h, and walks the rest of the way at 5 km/h. His total journey time is 1 hour. How far did Jacob run?

The answer is B, if you substitute x with 0 1 or 2 the result will always be 0

ANSWER

[tex]f(x) ={x}^{3} - 3 {x}^{2} + 2x[/tex]

EXPLANATION

If the polynomial function has zeros at 0,1 and 2

Then the polynomial can be written in factored form as:

F(x)=x(x-1)(x-2)

We expand to get,

[tex]f(x) =x({x}^{2} - 3x + 2)[/tex]

Expand further to obtain:

[tex]f(x) ={x}^{3} - 3 {x}^{2} + 2x[/tex]

The polynomial in descending powers of x is said to be in standard form .

The last choice is correct.

Answer: 9

Step-by-step explanation:

M=3 and the equation is 3m so your going to multiply. So the equation would be 3*3 and 3*3=9 so that's your answer

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}\\(x_ {1}, y_ {1}) :( 2,2)\\(x_ {2}, y_ {2}) :( 5,5)[/tex]

Substituting the points:

[tex]d = \sqrt {(5-2) ^ 2 + (5-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (3) ^ 2}\\d = \sqrt {9 + 9}\\d = \sqrt {18}\\d = 3 \sqrt {2}[/tex]

ANswer:

[tex]d = 3 \sqrt {2}[/tex]

Answer:

(D same size and same shape)​

Step-by-step explanation:

Congruent means the same size and shape.

Similar means the same shape, but not necessarily the same size

Answer:

The answer is : (D same size and same shape)​

Step-by-step explanation:

Two shapes or figures are called congruent, when they are identical. When the angles are equal in degrees, they are called congruent angles and when sides are congruent, this means they have the same length.Two polygons are congruent if they have the same size and shape or if their corresponding sides and angles are equal.

Therefore, option D is correct.

Answer: 29,500.

Step-by-step explanation: percentagecalculator.com

Answer:

y = 5x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 5, hence

y = 5x + c

The line passes through the y- axis at (0, 3) ⇒ c = 3

y = 5x + 3 ← equation of line

Answer:

8%

Step-by-step explanation:

Answer:

The length side of the original square banner was 9 ft

Step-by-step explanation:

Let

x-----> the length side of the original square banner

we know that

The new area of the banner is equal to

[tex]91=(x+4)(x-2)[/tex]

Solve for x

[tex]91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0[/tex]

Solve the quadratic equation by graphing

The solution is x=9 ft

see the attached figure

To determine the length of the original square banner, we can set up an equation using the given information and solve for the side length.

To solve this problem, let's first represent the length of the original square banner as x. According to the question, 4 feet is added to the width, so the width becomes x + 4. Also, 2 feet is subtracted from the height, so the height becomes x - 2. The area of a square is calculated by multiplying the side lengths, so we have (x + 4)(x - 2) = 91.

Expanding the equation, we get x² + 2x - 8 = 91. Rearranging the equation, we have x² + 2x - 99 = 0. This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula.

By factoring, we find (x + 11)(x - 9) = 0. So, x = -11 or x = 9. Since we cannot have a negative length for a banner side, we discard x = -11. Therefore, the length of the side of the original square banner is 9 feet.

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Answer:

The correct answer is  last option

Cos(55) = 11/x

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = opposite side/Adjacent side

From the figure we can see a right angled triangle, with one angle is 55 degree, one side is 11 and hypotenuse is x

To find the correct trigonometric formula

Here we have adjacent side of angle 55

Cos 55 = Adjacent side/Hypotenuse

Cos 55 = 11/x

Therefore the correct answer is last option

Answer:

False

Step-by-step explanation:

The equation x = c represents the equation of a vertical line parallel to the y- axis.

The equation y = c represents the equation of a horizontal line parallel to the x- axis

In both cases c is a constant

Hence x = - 2 is not parallel to the x- axis

Answer:

7.04 trillion = 7.04 x 10¹²

Step-by-step explanation:

Answer: 7.04 x 10^12

Step-by-step explanation:

Just took the test :)

Answer:

Step-by-step explanation:

[tex](f\circ f)(x)=f\bigg(f(x)\bigg)\\\\f\bigg(f(3)\bigg)\\\\\text{Calculate}\ f(3):\\\\f(3)=3^2-3=9-3=6\\\\f\bigg(f(3)\bigg)=f(6)=6^2-6=36-6=30[/tex]

k(3)=13(3)-2

k(3)= 39-2

Answer is k(3)= 37

ANSWER

[tex]k(3) = 37[/tex]

EXPLANATION

The given expression is

[tex]k(t) = 13t - 2[/tex]

We want to find k(3).

We substitute t=3 into the expression to get:

[tex]k(3) = 13(3) - 2[/tex]

We multiply out to get,

[tex]k(3) = 39- 2[/tex]

Simplify to get,

[tex]k(3) = 37[/tex]

Answer:

The second answer is correct.

Step-by-step explanation:

Distributive property means that you must multiply the number directly outside the parentheses to all the numbers inside the parentheses

Look at the image below for the work!

Hope this helped!

Using the Distributive Property to expand and evaluate an expression.

Given expression: (5 + 1)3

Step 1: Apply the Distributive Property to expand the expression:  (5 + 1)3 = 5 x 3 + 1 x 3

Step 2: Evaluate the expression: (5 + 1)3 = 15 + 3 = 18

y=0 because no matter what x value you have, y will always be 0

Y=0 because the y-axis of the line is 0

The system of equations to represent the concession stand sales situation is 3H + 4B = 184 for the total sales, and H = B + 10 for the quantity relationship, where H is the number of hot dogs sold, and B is the number of burgers sold.

To represent this situation with a system of equations, let's denote the number of hot dogs sold as H and the number of burgers sold as B. According to the problem, hot dogs are sold at $3 each and burgers at $4 each, and the stand made $184 in total. Also, we are told that 10 more hot dogs than burgers were sold at the game.

We can create two equations to represent this scenario:

These two equations form the system that can be solved to find the number of hot dogs and burgers sold.

Answer:

c

Step-by-step explanation:

the formula is [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1}}[/tex]

When we plug that in we get [tex]\frac{-3-2}{6- (-4)} = \frac{-5}{10} = -\frac{1}{2}[/tex]

Hope this helps!

Answer:

x = 5

Step-by-step explanation:

You have a right triangle, so you can use the Pythagorean Theorem.

a^2 + b^2 = c^2

x^2 + 12^2 = 13^2

x^2 + 144 = 169

x^2 = 25

x = 5

Answer: x = 5

Answer:

just do 13 time 12

Step-by-step explanation:

ANSWER

The missing probability is 0.15

EXPLANATION

From the given probability distribution table.

P(1)=0.30

P(2)=0.40

P(3)=0.15

P(4)=?

For for this to represent a probability distribution function,then the sum of all the probabilities must be equal to 1.

P(1)+P(2)+P(3)+P(4)=1

This implies that,

0.30+0.40+0.15+P(4)=1

0.85+P(4)=1

P(4)=1-0.85

P(4)=0.15

Therefore the missing probability is 0.15

Answer:

The desired equation is y = -2x - 4

Step-by-step explanation:

The general slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Starting from that, substitute the given values for m, x and y and calculate b:

6 = -2(-5) + b.  Then 6 = 10 + b, and b = -4.

The desired equation is y = -2x - 4.

Answer:

30°

Step-by-step explanation:

Segment MP is the diameter of the circle, hence angle MOP has the measure of 180°.

Angles MON and NOP are supplementary angles (add up to 180°). Thus,

m∠MON+m∠NOP=180°

m∠MON=180°-m∠NOP

m∠MON=180°-150°=30°.

Angle MON is the central angle subtended on the arc MN. Thus, the measure of the arc MN is 30°.

Answer:

Step-by-step explanation:

It's important to know that the whole arc of a circle is 360°.

So, if MP is a diameter, that means it divides the circle in two equal parts of 180° each.

Now, one half of this arc is formed by MN and 150°, so we can formulate the expression

[tex]MN+150\° = 180\° \\MN= 30\°[/tex]

Therefore, the arc MN is 30°.

Answer: -5, and 5

Step-by-step explanation: an absolute value can only be positive. So -5 and 5 are the only answers that will give you 5.

Answer:

B and D.

Step-by-step explanation:

–15

–5

0

5

15

Absolute Value  Assignment

Finding Absolute Value

Answer:

Part 1) The x-intercept is the point (-5,0)

Par 2) The y-intercept is the point (0,-17.5)

Step-by-step explanation:

step 1

Find the x-intercept

we know that

The x-intercept is the value of x when the value of y is equal to zero

Observing the table

For x=-5, y=0

therefore

The x-intercept is the point (-5,0)

step 2

Find the equation of the line

Find the slope m

we have

(-7,7) and (-5,0)

[tex]m=(0-7)/(-5+7)\\ m=-3.5[/tex]

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-3.5[/tex]

point (-5,0)

substitute

[tex]y-0=-3.5(x+5)[/tex]

[tex]y=-3.5(x+5)[/tex]

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

[tex]y=-3.5(0+5)[/tex]

[tex]y=-17.5[/tex]

therefore

The y-intercept is the point (0,-17.5)

Answer:

500 Elm: Cafe

524 Elm: Grocery

538 Elm: Boutique

544 Elm: Dance studio

Step-by-step explanation:

We know that the dance studio has the highest address, so 544.

For the others let's examine the possibilities.

The boutique is between the cafe and the studio, that means the following are possible:

Boutique can be at either 524 or 538, cannot be at 500 (since cafe has to be on the its left.

Cafe can be 500 or 524, cannot be 538 since boutique has to be between cafe and studio.

The grocery is between the cafe and boutique. Meaning the grocery cannot be 500 nor 538, since it has to be in the middle of the 3 remaining businesses.  So, grocery is at 524.

Meaning the Cage is at 500 and the boutique is at 538.

Answer:

B

Step-by-step explanation:

On edge

To build a school;

20 workers -> 18 days.

So 1 worker -> 18/20 days.

So; 12 workers -> (12×18)/20 days.

-> (12×9)/10 days

->10.8 days.

so 10.8 days is your answer.

Hope it helps...

Regards;

Leukonov/Olegion

If 20 workers can build a school in 18 days, how many days will it take 12 workers to build the same school?

In this question we are provided that 20 workers can build a school in 18 days. We are asked to calculate how many days will 12 workers will take to do the same work.

We can solve this question using two methods :

[tex] \small\bf{ Unitary \: Method}[/tex]

20 workers can build a school in 18 days

1 worker can build a school in 20 × 18 days

12 workers can build a school in [tex]\dfrac{20 × 18 }{12}[/tex] = 30 days.

[tex] {{\rule{40mm}{4pt}}}[/tex]

[tex] \small\bf{ Method \: of \: proportion }[/tex]

Let us assume that 12 workers can finish the work in x days.

[tex]\begin{array}{c|c} \bf{Number \: of \: workers }& \bf{Number \: of \: days}\\ 20 & 18 \\ 12 & x\end{array}[/tex]

Ratio of workers = Inverse ratio of days

[tex] \small\sf{ 20 : 12 :: x : 18}[/tex]

Product of mean = Product of extreme

[tex] \small\rm{ 12 \times x = 20 \times 18}[/tex]

[tex] \small \rm{ \dfrac{20 \times 18}{12} = 30 \: days}[/tex]

[tex] \rule{72mm}{5pt}[/tex]

Answer:

1/4

Step-by-step explanation:

because if you use the process of breaking down the numbers they will end up going down to simplest form.

Answer:

3/12 = 1/4

Step-by-step explanation:

If we know 12 is equal to a fraction with the denominator of 4, we can divide 12 by 4 and get 3. This means we must also divide the numerator by 3 to get 3/3 = 1. Another way to solve this is to cross multiply. If 3/12 = _/4, we multiply the numerator of the first fraction by the denominator of the second fraction. Then, we get 12. Divide the 12 by the denominator of the first fraction to get 12/12. This will give you an answer of 1 as well.

Answer:

To the right we have 62.6 while to the left we have 49.4

Step-by-step explanation:

A normal distribution is usually symmetric with respect to the mean. The mean of the distribution is also the mode as well as the median.

The general formula for points that lie n standard deviations away from the mean on either sides of the mean is given by the formula;

mean ± n(σ)

where σ is the standard deviation of the distribution;

Two standards deviations from the mean imply that n = 2;

56 ± 2(3.3)

56 ± 6.6

To the right we have 62.6 while to the left we have 49.4

Answer:

The measure of angle x is [tex]64.4\°[/tex]

Step-by-step explanation:

To find the measure of angle X, apply the law of cosines

The law of cosines states that

[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]

In  this problem we have

[tex]a=19\ cm[/tex]

[tex]b=25\ cm[/tex]

[tex]c=24\ cm[/tex]

[tex]C=x\°[/tex]

substitute

[tex]24^{2}=19^{2}+25^{2}-2(19)(25)cos(C)[/tex]

[tex]576=986-950cos(C)[/tex]

[tex]cos(C)=(986-576)/950[/tex]

[tex]C=arccos[(986-576)/950]=64.4\°[/tex]

Therefore

The measure of angle x is [tex]64.4\°[/tex]