Find the missing base of the triangle when the area is 94.5cm2

Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.

Looing at ΔOAB and ΔOEF

It is clear that

OB = OF (O is the midpoint)

∠OBA = ∠OFE = 90°

Therefore

∠AOB = ∠EOF (Vertically Opposite Angles)

⇒ ΔOAB ≅ ΔOEF and

∠ A ≅ ∠E.

QED

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Using a dot plot, it is found that the number of dots of each point are given as follows:

The dot plot shows the number of times each measure appears in the data-set.

In this problem, one measure has a value of 1/8, hence:

The value [tex]\frac{1}{8}[/tex] will have one dot above it.

Two measures have a value of 1/4, hence:

The value [tex]\frac{1}{4}[/tex] will have two dots above it.

Three measures have a value of 3/8, hence:

The value [tex]\frac{3}{8}[/tex] will have three dots above it.

Five measures have a value of 1/2, hence:

The value [tex]\frac{1}{2}[/tex] will have five dots above it.

Two measures have a value of 5/8, hence:

The value [tex]\frac{5}{8}[/tex] will have two dots above it.

Three measures have a value of 3/4, hence:

The value [tex]\frac{3}{4}[/tex] will have three dots above it.

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Answer:

1 2 3 5 2 3

Step-by-step explanation:

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

[tex]\rm x=y+z[/tex]

Plug this value in the equation (2) and (3):

[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

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Answer:

tanD =4/7

Step-by-step explanation:

tanD = P/B

Where P=4 and B=7

So;

tanD=4/7

Celina says true that each of the following expressions is actually a binomial expression.

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a.  5abc - 2a² + 6abc = 11abc - 2a²

The is a binomial expression.

b.  5x³∙2x² - 10x⁴ + 3x⁵ + 3x∙(-2) x⁴ = 7x⁵ - 10x⁴

The is a binomial expression.

c.  (t+2)² - 4t = t² + 4

The is a binomial expression.

d.  5(a - 1) - 10(a - 1) + 100(a - 1) = 95a - 95

The is a binomial expression.

e.  (2πr - πr² )r - (2πr - πr²)∙2r = -2πr² + πr³

The is a binomial expression.

Celina says true that each of the following expressions is actually a binomial expression.

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Answer:

its the Pentagon, the other shaps have 2 lines if symmetry

The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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Answer:

D. 105

Step-by-step explanation:

500-270, there's 230 total 2 head.

270-100 of one head, is 170 purple one head. 170+125 purple equals 295.

296 subtract from 500 total is 205 for total green.

205-100, 105 2 head.

im not sure I'd need to see the figure

610

Step-by-step explanation:

The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the  point where the velocity the body is zero.

Given the function that represent the height of the swimmer as  h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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see the attachment photo!

Answer:

No

Step-by-step explanation:

Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.

Answer:

false

Step-by-step explanation:

Answer: y - 17 = -2(x-7)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = 9+17/-6-7

   = 26/-13

   = -2

y1 = -17

x1 = 7

y - 17 = -2(x-7)

The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

The general equation of a straight line is-

y = mx + c

where, m is the gradient and is given by y₂ - y₁/x₂ - x₁

and, c is the value where the line cuts y-axis.

Now it is given that the line passes through points (−6,9) and (7,−17)

Therefore we have,

x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17

So, the slope m of the line is given as,

m = (y₂ - y₁)/(x₂ - x₁)

Put the values,

m = (-17 - 9)/(7 - (-6))

m = -26/7+6

m = -26/13

m = -2

Thus, the equation parallel to the line will be given as:

y - y₁ =  m(x - x₁)

y - 9 =  -2{x - (-6)}

y - 9 =  -2(x + 6)

y =  -2x - 12 + 9

y =  -2x - 3

Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

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Step-by-step explanation:

1) x+6 =4

x. =4-6

x. =-2

2) x-(-4) =-6

x+ 4. =-6

x. =-6-4

x. =-10

3)2(x-1)=-200

2x-2 =-200

2x. = -200+2

2x. = -198

x. = -198/2

x. = -99

4)2x+(-3) =-23

2x-3. =-23

2x. =-23+3

2x. =-20

x. =-20/2

x. = -10

Answer:

2/9

Step-by-step explanation:

8/12 you pick an office worker

4/12 chance you pick a manager

8/12 multiplied by 4/12 is 32/144

We can simplify this to 16/72

We can simplify this to 8/36

We can simplify this to 4/18

We can simplify this to 2/9

It makes that every time we flip a fair the probability of flipping tails is 50%.

Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. If it is equally likely and unlikely that the event would happen, it would have a probability of 0.5

Probability of flipping tails = number of tails / number of sides

1/2 = 0.5 = 50%

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Answer: The value of x is 3.5

Explanation:

Equation:

y = 2x - 7

When the equation's Line intersects the x-axis, the value of y shall be always 0

Insert y = 0, to find x intercept

⇒ 0 = 2x - 7

⇒ 2x - 7 = 0

⇒ 2x = 7

⇒ x = 3.5

So coordinates: (x, y) → (3.5, 0)

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

Answer:

A

Step-by-step explanation:

height (y-axis) = constant × width (x-axis)

let's look at the point coordinates.

remember, an ordered pair of point coordinates consists of an x value and an associated (typically calculated by a function) y value.

we see that all y values are half of the x values (3 and 1.5, 2 and 1, 7 and 3.5, 8 and 4).

so, the constant in our equation is responsible for returning half of the x value back as the y value.

what constant factor turns a number in half ?

x × c = x/2

c = 1/2

and so, A is the right answer.

Considering the given quadratic equation, the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the equation is given by:

h(t) = -(t - 12)² - 81.

The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

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Considering that 12 is a root of the function, the value of coefficient Q is of 12.

It means that f(x) = 0.

In this problem, the function is given by:

f(x) = x² - 13x + q.

Since 12 is a root, we have that f(12) = 0, hence:

12² - 13 x 12 + q = 0

q - 12 = 0.

q = 12.

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The data values that are outliers are 4 and 56.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.

In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.

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Answer:

1/3

Step-by-step explanation:

[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]

Based on the properties of a kite, the statement that is true is: D. KPE = TPE.

A kite is a quadrilateral in which its diagonals intersect at right angles.

Also, the non-vertex angles of a kite are congruent, that is they have equal measure.

Angle KPE and angle TPE in the given kite are right angles formed at the point of intersection of the two diagonals of the kite. They both equal 90 degrees.

Therefore, the true statement is:

D. KPE = TPE

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Answer: 8

Step-by-step explanation:

The discriminant is [tex]b^2-4ac[/tex]

in the equation:

[tex]-x^2+4x-2[/tex]

A = -1, B = 4, C = -2

plug into equation

[tex]4^2-4(-1)(-2)[/tex]

[tex]16-8[/tex]

⇒ [tex]8[/tex]

(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

Answer:

[tex]\frac{100}{a}[/tex]

Step-by-step explanation:

Hello!

a% is the same as [tex]\frac a{100}[/tex].

a% of a can be found by multiplying them both, giving us [tex]\frac {a^2}{100}[/tex]

The value of the expression is [tex]\frac{100}{a}[/tex]

Step-by-step explanation:

remember a few things :

a × -1 = -a

-a × -1 = a

-1 × -1 = 1

1 × a = a

therefore,

-1 × -1 × a = 1 × a = a

and finally

c × (a + b) = c×a + c×b

so, we can say

(1 - 5) = -1 × -1 × (1 - 5) =

= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =

= -1 × (5 - 1) = -(5 - 1)