the diagram shows a triangle.
all the measurements are in cm
the perimeter of the triangle is 70cm
the area of the triangle is Acm squared
work out the value of A​

Answer:

The needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]

Step-by-step explanation:

The given equation is of the form [tex]p(x) = ax^2 + bx + c[/tex]

The given solutions of the equations are:

x = 3 +i, x = 3 - i

Now, if x = a is the zero of the polynomial p(x)

⇒(x -a ) is the root of the given polynomial.

⇒ (x - ( 3+i)) and (x - ( 3+i)) are the given roots for p(x)

P(X) = PRODUCT OF ALL ROOTS

⇒ p(x) = (x - ( 3+i))(x - ( 3-i))  = ( x-3 -i)(x -3+i)

Now, [tex](a-b)(a +b) = a^2 - b^2\\\implies ( (x-3)-i)((x-3)+i) = (x-3)^2 - (i)^2 = x^2 +9 - 3x -(-1)\\= x^2 +10 - 3x\\\implies p(x) = x^2- 3x + 10[/tex]

Hence, the needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]

Answer:

The average of this pie chart is 33 1/3.

Step-by-step explanation:

To find the average (or mean) of this pie chart, we simply add all the numbers together then divide the sum by however many numbers there are:

71.4 + 14.3 + 14.3 = 100

100  ÷ 3 = 33.333... or 33 1/3

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

a = 14

Step-by-step explanation:

Given

9 + a = 23 ( subtract 9 from both sides )

a = 14

Answer:

9+14=23

Step-by-step explanation:

you subtract 9 from 23 and you get 14 so there for the answer is 9+14=23

The minimum possible area of the rectangle is 19.25 m² and the maximum possible area is 29.25 m².

To find the minimum and maximum possible areas of the rectangle, we need to consider the possible values that the length and width can take.

Given that the measured dimensions are 6 m by 4 m to the nearest whole unit, the minimum possible length would be 5.5 m (6 m - 0.5 m) and the minimum possible width would be 3.5 m (4 m - 0.5 m).

Similarly, the maximum possible length would be 6.5 m (6 m + 0.5 m) and the maximum possible width would be 4.5 m (4 m + 0.5 m).

To calculate the minimum and maximum possible areas, we multiply the minimum and maximum possible lengths by the minimum and maximum possible widths respectively. The minimum possible area would be 5.5 m x 3.5 m = 19.25 m² and the maximum possible area would be 6.5 m x 4.5 m = 29.25 m².

Answer:

slope = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ )= (3, 4) ← 2 points on the line

m = [tex]\frac{4-0}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]

Answer:

11

Step-by-step explanation:

Using the order of operations, that is multiplication before addition/ subtraction.

Given

6 + 2 × 3 - 1 ← evaluate multiplication

= 6 + 6 - 1 ← evaluate from left to right

= 12 - 1

= 11

He has been withdrawing money for 69 days.

Step-by-step explanation:

Amount of credit card = $5000

Let,

x be the number of days

Amount after withdrawing $45 each day for x days = $1895

Amount left = Total amount - Withdrawal amount per day * number of days

1895 = 5000 - 45*x

[tex]1895=5000-45x[/tex]

Solving for x;

[tex]1895-5000=-45x\\-3105=-45x\\-45x=-3105[/tex]

Dividing both sides by -45

[tex]\frac{-45x}{-45}=\frac{-3105}{-45}\\x=69[/tex]

He has been withdrawing money for 69 days.

Keywords: subtraction, division

Learn more about subtraction at:

#LearnwithBrainly

Because of the answers that you gave I'm going to assume the radians were 3pi/4. That would be A, 135 degrees.

If this is the wrong amount of radians please let me know.

The radian measures of the given degree measures are 3π / 4 Rad, π Rad, 3π / 2 Rad and 2π

One radian is the measure of a central angle subtended by an arc that is equal in length to the radius of the circle. When no symbol is used, radians are assumed. When degrees are the unit of angular measure, the symbol "°" is written. Note that the radian is a derived unit in the International System of Units (SI).

Given are some degree measurements, 135° 180° 270° 360°, we need to convert them into radians.

Since, we know that,

1 Rad = 1 Deg × π / 180

Therefore,

1) 135° = 135 × π / 180

= 3π / 4 Rad

2) 180° = 180 × π / 180

= π Rad

3) 270° = 270 × π / 180

= 3π / 2 Rad

4) 360° = 360 × π / 180

= 2π

Hence, the radian measures are 3π / 4 Rad, π Rad, 3π / 2 Rad and 2π

Learn more about radians, click;

https://brainly.com/question/7721249

#SPJ2

Answer:

9/10

Step-by-step explanation:

Final answer:

The improper fraction [tex]\frac{19}{10}[/tex] is equal to the mixed number [tex]1\frac{9}{10}[/tex], where 1 is the whole number and [tex]\frac{9}{10}[/tex] is the proper fraction remainder after division.

Explanation:

The improper fraction [tex]\frac{19}{10}[/tex] can be converted into a mixed number by dividing the numerator by the denominator. The division [tex]\frac{19}{10}[/tex] equals 1 with a remainder of 9. Therefore, the mixed number is [tex]1\frac{9}{10}[/tex]. This illustrates that any improper fraction can be expressed as a combination of a whole number and a proper fraction, where the numerator is smaller than the denominator.

Answer:

B) (3/10)/(7/9)=(3/10)(9/7)

Step-by-step explanation:

Answer:

a(b+c) = axb + axc

3(3+5)= 3x3 + 3x5

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

The ratio of Han's measurements and Tyler's measurements corresponds with polenta measurement

Given:

Polenta:

Cups of water = 5

Cornmeal = 2

Ratio of cups of water to cornmeal = 5 : 2

= 5/2

= 2.5

Han:

Cups of water = 3

Cornmeal = 1 1/5

= 6/5

Ratio of cups of water to cornmeal = 3 : 6/5

= 3 ÷ 6/5

= 3 × 5/6

= 15/6

= 2.5

Tyler:

Cups of water = 7 1/2

= 15/2

Cornmeal = 3

Ratio of cups of water to cornmeal = 15/2 : 3

= 15/2 × 1/3

= 15/6

= 2.5

Therefore, the ratio of Han's measurements and Tyler's measurements corresponds with polenta measurement.

Read more:

https://brainly.com/question/3796978

Final answer:

The question involves mathematical ratios to determine the correct proportions for a polenta recipe. By setting up proper proportions, we confirm that Han's and Tyler's calculations for the amount of cornmeal and water needed are correct.

Explanation:

The question discusses proportions used in a recipe which relates to mathematical ratios. Han and Tyler are trying to determine how much cornmeal and water they need for polenta based on a recipe that calls for a specific ratio of these ingredients. To solve this, we must set up a proportion that maintains the constant ratio given by the recipe.

For Han's statement, since the recipe calls for 5 cups of water for every 2 cups of cornmeal, we can set up the following proportion:

5 cups water / 2 cups cornmeal = 3 cups water / x cups cornmeal

Multiply across the equal fractions (5 * x = 2 * 3)

x = 6/5 or 1.2 cups cornmeal, which confirms Han's statement as correct.

For Tyler's statement, using the same ratio:

2 cups cornmeal / 5 cups water = 3 cups cornmeal / x cups water

Multiply across the equal fractions (5 * 3 = 2 * x)

x = 15/2 or 7.5 cups water, which confirms Tyler's statement as correct as well.

Answer:

576

Step-by-step explanation:

8*8 = 64

If dimensions are tripled, you get 24. 24*24 = 576

Answer:

576

Step-by-step explanation:

A=L*W

8*8=64

8*3=24

24*24=576

The equation of line parallel to y = -5x + 6 and passes through the point (-4, -1) is y = -5x -21

Given that, a line passes through (-4, -1) and it is parallel to y = -5x + 6

We have to find the line equation of that line.

Now, as we can see given line equation is in slope intercept form y = mx + c

where "m" is the slope of line and "c" is the y-intercept

So, by comparison, slope of that line is m = -5

We know that slopes of two parallel lines are equal

And as the required line is parallel to given line, it will also have the same slope.

Then, slope of our line = -5

And let us find the line equation point slope form

y – a = m(x - b) where (b, a) is a point on the line

So, line equation is y – (-1) = -5(x – (-4))

y + 1 = -5(x + 4)  

y + 1 = -5x – 20  

y = -5x -20 – 1

y = -5x -21

Thus the equation of required line is y = -5x -21  

The equation of the line parallel to y = -5x + 6 and passing through (-4, -1) is y = -5x - 21, which is determined using the point-slope form of a line with the given point and the parallel line's slope.

To find an equation of a line that is parallel to the given line y = -5x + 6 and passes through a specific point (-4, -1), we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Since parallel lines have the same slope, the line we are looking for will also have a slope of -5. Using the point (-4, -1) and the slope -5, we can substitute these values into the point-slope form:

y - (-1) = -5(x - (-4))
y + 1 = -5(x + 4)
y = -5x - 20 - 1
y = -5x - 21

Thus, the equation of the line is y = -5x - 21.

Answer:

-17

Step-by-step explanation:

3 + 4(-5)

= 3-20

= -17

Hope this helps!

Answer:

-17.

Step-by-step explanation:

3 + 4 x (-5)

= 3 + -20

= 3 - 20

= -17.

Answer:

the first diagram (circled one in the attached figure)

Step-by-step explanation:

number of pickle slices in each burger = [tex]\frac{78}{26} = 3[/tex] (I hope you know how to find this)

The diagram is nothing but expressing fraction diagrammatically.

The fraction is 78 divided by 26. So assume bar of size 78. Now divide it into 26 equal parts. The same is shown in the diagram.

For example: [tex]\frac{1}{4}[/tex] of a chocolate bar is nothing but one piece when you divide the chocolate bar into four equal parts.

Answer:

P(E or F) = 0.75

Step-by-step explanation:

Given;

P(E)=0.30

P(F)=0.45

We need to find probability of P(E or F).

Now by General theorem of probability addition theorem:

P(E or F) = P(E) + P(F) - P(E and F)

For mutually exclusive events, P(E and F) = 0

So, P(E or F) = P(E) + P(F) = [tex]0.3 +0.45 = 0.75[/tex]

Hence P(E or F) = 0.75

Probabilities are used to determine the chances of an event.

The probability of P(E or F) is 0.75

The parameters are given as:

[tex]\mathbf{P(E) = 0.30}[/tex]

[tex]\mathbf{P(F) = 0.45}[/tex]

[tex]\mathbf{P(E\ or\ F) = P(E) + P(F)}[/tex]

So, the equation becomes

[tex]\mathbf{P(E\ or\ F) = 0.30 + 0.45}[/tex]

[tex]\mathbf{P(E\ or\ F) = 0.75}[/tex]

Hence,  the probability of P(E or F) is 0.75

Read more about probabilities at:

https://brainly.com/question/17136647

Answer:

The answer is A

Step-by-step explanation:

Answer:

8/12

Step-by-step explanation:

2/3 x 4= 8/12

Answer:

4/6

The drawing will help

Answer:

[tex]\displaystyle 161[/tex]

Step-by-step explanation:

[tex]\displaystyle 159 = \frac{477}{3} \\ \\ 318 = 157 + 161 \\ \\ 161, 159, 157[/tex]

I am joyous to assist you anytime.

Answer:

x

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers.

Answer:

x

Step-by-step explanation:

Answer:

[tex]m\angle B=54^{\circ}[/tex]

[tex]m\angle BAD=36^{\circ}[/tex]

[tex]m\angle CDA=90^{\circ}[/tex]

[tex]BAC=72^{\circ}[/tex]

Step-by-step explanation:

Given:

[tex]\overline{AB}\cong \overline{AC},[/tex]

[tex]\overline{AD}[/tex] bisects angle BAC

[tex]m\angle C=54^{\circ}[/tex]

Triangle ABC is isosceles triangle, because [tex]\overline{AB}\cong \overline{AC}.[/tex] Angles adjacent to the base of isosceles triangle ABC are congruent.

Hence,

[tex]m\angle C=m\angle B=54^{\circ}[/tex]

The sum of the measures of all interior angles is 180°, so,

[tex]m\angle B+m\angle C+m\angle BAC=180^{\circ}\\ \\m\angle BAC=180^{\circ}-2\cdot 54^{\circ}=72^{\circ}[/tex]

Since [tex]\overline{AD}[/tex] bisects angle BAC, angles BAD and CAD are congruent by definition of angle bisector. So,

[tex]m\angle BAD=m\angle CAD=\dfrac{1}{2}m\angle BAC=\dfrac{1}{2}\cdot 72^{\circ}=36^{\circ}[/tex]

AD ia angle bisector in isosceles triangle drawn to the base, so it is the height. Thus, AD and BC are perpendicular. So,

[tex]m\angle CDA=90^{\circ}[/tex]

Answer:

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.66

Step-by-step explanation:

Let us assume the cost of 1 pound salmon = $ m

So the cost of 1 pound of 1 pound swordfish cat = $ ( m - 0.20)

Now, the Amount of salmon purchased  = 2 1/2 pounds

[tex]2\frac{1}{2}  = 2 + \frac{1}{2} = 2 + 0.5 = 2.5[/tex]

So, the amount of salmon purchased = 2.5 pounds

Cost of buying 2.5 pounds = 2.5 x ( 1 pound cost)

= 2.5 ( m) = $ 2.5 m  ...... (1)

Also, the Amount of swordfish purchased  = 1 1/4 pounds

[tex]1\frac{1}{4}  = 1 + \frac{1}{4} = 1 + 0.25 = 1.25[/tex]

So, the amount of swordfish purchased = 1.25 pounds

Cost of buying 1.25 pounds = 1.25 x ( 1 pound cost of swordfish)

= 1.25 ( m - 0.20) = $ 1.25 m - 0.25       .... (2)

Now, the combined cost paid  = $ 31.25

⇒Cost of buying (2.5 pounds salmon  +  1.25 pounds swordfish) = $ 31.25

or, 2.5 m +   1.25 m - 0.25  = 31.35       (from (1) and (2))

or, 3.75 m = 31.60

or, m = 31.60/3.75 =  8.43

⇒ m = $8.43

So, the cost of 1 pound salmon = m = $8.43

and the cost of 1 pound swordfish = m - 0.20 = $8.43 - 0.20 = $ 8.23

Hence, the combined cost  1 pound of salmon and 1 pound of swordfish = $8.43 + $ 8.23 =  $ 16.66

Answer:

3

Step-by-step explanation:

Greatest Common Factor is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.

3 is divisible by 9, 15, and 36.

the answer is m = 200

Answer: s = 1.44

Step-by-step explanation:

11 - 18*s = -15

-18*s = -15 - 11

-18*s = -26

18*s = 26

s = 26/18

s = 13/9

s = 1.44

The equation of a circle if the ends of the diameter are (18,-13) and (4,-3)​ is [tex](x-11)^{2}+(y+8)^{2}=74[/tex]

Given that ends of diameter are (18, -13) and (4, -3)

To find the equation of circle, let us first find the center (h, k) of the circle

We know that the center of the circle lies in the center of the diameter also. In order to find the center, get the average of both x and y

[tex]\mathrm{c}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

[tex]\begin{array}{l}{c=\frac{18+4}{2}, \frac{-13-3}{2}} \\\\ {c=\frac{22}{2}, \frac{-16}{2}} \\\\ {\mathrm{c}=(11,-8)}\end{array}[/tex]

These are the coordinates of the center of the circle

Now we need to find the radius, we need the center (h, k) and one of the given points (4, -3):

The equation of circle is given as:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

[tex]\begin{array}{l}{(4-11)^{2}+(-3-(-8))^{2}=r^{2}} \\\\ {(-7)^{2}+(-3+8)^{2}=r^{2}} \\\\ {(-7)^{2}+(5)^{2}=r^{2}} \\\\ {49+25=r^{2}} \\\\ {r=\sqrt{74}}\end{array}[/tex]

So the equation of the circle is:

[tex]\begin{array}{l}{(x-11)^{2}+(y-(-8))^{2}=(\sqrt{74})^{2}} \\\\ {(x-11)^{2}+(y+8)^{2}=74}\end{array}[/tex]

[tex]\frac{1}{2}[/tex] of the grandmother's lawn Dan can mow per gallon.

Option C

Solution:

Given that, mowing [tex]\frac{1}{4}[/tex] uses [tex]\frac{1}{2}[/tex] gallon of gas.

To find: The fraction of the lawn can Dan mow per gallon

According to unitary method,

[tex]\frac{1}{2}[/tex] gallon of gas is required to mow [tex]\frac{1}{4}[/tex] of lawn that is [tex]\frac{1}{2}\rightarrow \frac{1}{4}[/tex]

Therefore, 1 gallon of gas will be required to mow [tex]\frac{1}{2}\times2\rightarrow \frac{1}{4}\frac2[/tex]

[tex]\Rightarrow1 \text{ gallon }\rightarrow \frac{1}{2} \text{ of lawn}[/tex]

Therefore, one gallon will be enough to mow [tex]\frac{1}{2}[/tex] of lawn.

Unitary method:

The unitary method is a technique to solve a problem by finding the value of a single unit first, and then finding the required value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.