If (a, -8) is a solution to the equation -a = 4b - 7 what is a?

Answer:

Step-by-step explanation:

Point R is the mid point of side FE Using mid point formula coodinates of F are (3a,b)

In triangle DEF, DF = base = 4a and height = 2b.

Hence area of triangle DEF = 1/2 hy = 4ab

In triangle QRP, base QR = line joining mid points of sides DE and EF

= 1/2 (DF) = 2a

Height =b

So area of triangle DEF = 1/2 (2a)b = ab

i.e. Area of triangle DEF = 4 times triangle QRD

It follows that in an isosceles triangle, if QR is the mid points of isosceles sides, then triangle QRD has 1/4 times area of triangle DEF

Answer:

[tex]\frac{8}{100}[/tex]

Step-by-step explanation:

Given :Number = 24.387

To Find : What is the value of the 8 in the number 24.387?

Solution:  

The first digit after the decimal point is called the tenths place value = [tex]\frac{1}{10}[/tex]

The second digit after the decimal point is called hundredths place value= [tex]\frac{1}{100}[/tex]

The third digit after the decimal point is called thousandths place= [tex]\frac{1}{1000}[/tex]

Number = 24.387

Since 8 is The second digit after the decimal point

So, The place value of 8 is hundredths

So, the value of 8 in fraction = [tex]\frac{8}{100}[/tex]

Hence The value of the 8 in the number 24.387 is  [tex]\frac{8}{100}[/tex]

The value of the 8 in the number 24.387 as a simplified fraction is 4/5.

The 8 in the number 24.387 is in the tenths place, so it represents 8 out of 10.

We can write this as a fraction as follows:

8 / 10

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2.

The greatest common divisor of 8 and 10 is 2. Dividing both the numerator and denominator by 2, we get:

(8 / 2) / (10 / 2) = 4 / 5

Therefore, the value of the 8 in the number 24.387 as a simplified fraction is 4/5.

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width = perimeter/2 - length

w = 74/2 - 5 = 32

32/4 = 8 - 3 = 5

The length of the rectangle is 5.

The width of the triangle is 32

As per the given values, the length of the rectangle is 29 meters and the width is 8 meters.

To find the length and width of the rectangle, we can use the information given: the length is 3 meters less than four times the width, and the perimeter is 74 meters. Let's assume the width is 'w' meters. So, the length would be '4w - 3' meters. The perimeter of a rectangle is found by adding the lengths of all its sides, which in this case is twice the length plus twice the width.

We can set up an equation to solve for 'w': 2(4w - 3) + 2w = 74. Solving this equation will give us the width of the rectangle, and we can substitute that value back to find the length.

Step 1: Set up the equation:

2(4w - 3) + 2w

= 74.

Step 2: Simplify the equation:

8w - 6 + 2w

= 74.

Step 3: Simplify further:

10w - 6 = 74.

Add 6 to both sides.

Step 4: Continue to simplify:

10w = 80.

Divide both sides by 10.

Step 5: Solve for 'w':

w = 8.

The width of the rectangle is 8 meters.

Step 6: Find the length

= 4w - 3

= 4(8) - 3 = 32 - 3

= 29 meters.

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Answer:

11. O = (-1, 5/2); 12. H = (1,4)  

Step-by-step explanation:

11. Circumcentre

Your points form the vertices of a right triangle (see image below).

The circumcentre (O) of a right triangle must be at the midpoint of the hypotenuse.

Your hypotenuse has the ends at (-3,4) and (1,1), so

O = ((-3 + 1)/2),(4 + 1)/2))

O = (-2/2,5/2)

O = (-1, 5/2)

===============

12. Orthocentre

The orthocentre (H) of a right triangle is the vertex at the right angle.

Your right angle is at (1, 4), so

H= (1,4)

Answer:

Step-by-step explanation:

Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle! so A=1/2(6)(h). 1/2 times six is 3 so you have A=3h, subtract 3 and your awnser is 3A=h divide by 2 H= 1.5

Answer:

Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle! so A=1/2(6)(h). 1/2 times six is 3 so you have A=3h, subtract 3 and your awnser is 3A=h divide by 2 H= 1.5 I dont understand how this answers a question wit showing full steps

Step-by-step explanation:

Answer:

The 52nd term is -125

Step-by-step explanation:

The formula for an arithmetic sequence is

an = a1+d(n-1)

where a1 is the first term and d is the common difference.

a1 = 28

d = 25-28 = -3

Let's check  19-22 = -3  so the common difference is correct

an = 28 - 3(n-1)

We want to find the 52 term  so n = 52

a52 = 28 -3 (52-1)

a52 = 28 -3(51)

a52 = 28 -153

a52 = -125

Answer:

133

Step-by-step explanation:

Answer:

48,000. Look at the tens place, If the number is 5 or higher then you round up, if its 4 or lower the hundreds place stays the same. Since the number in the tens place is higher than 4 you round up, meaning you would add 1 to 9 which give you ten. You would carry that ten over, giving you 48,000

The correct answer is 48,000.

To round the number 47,963 to the nearest hundreds:

Identify the digit in the tens place, which is 6.

Since the digit in the tens place is greater than or equal to 5, round up the hundreds place.

The current digit in the hundreds place is 9.

Rounding up the hundreds place from 9 results in increasing it to the next number, which is 10.

When the hundreds place increases to 10, it affects the thousands place as well:

The 7 in the thousands place becomes 8, because adding 1 to 9 in hundreds place essentially adds 1,000 to the overall number.

Set all digits to the right of the hundreds place to zero.

Thus, 47,963 rounded to the nearest hundreds becomes 48,000.

This process ensures accurate rounding based on standard rounding rules.

Answer:

Step-by-step explanation:

Given that a box has cards numbered 1 ,2,3

Also a bag has three balls labelled A, B and C

Sample space = {(1,A)(1,B)(1,C) (2,A)(2,B)(2,C)}  n(S) = 9

Mary will randomly pick up a card from the 3 cards and also pick up a ball from the bag of 3 balls.

The sample space contains the combination of letter on the card and number on the ball.

Event that the number chosen is 1 is

{(1,A)(1,B)(1,C)}:  n(event of choosing 1)=3

Answer:

70 feet per minute.

21 minutes

1890 feet

Step-by-step explanation:

(350 ft) / (5 min) = 70 ft/min

(1470 ft) / (70 ft/min) = 21 min

(70 ft/min) * (27 min) = 1890 ft

Answer:

The theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Step-by-step explanation:

Getting x successes out of n trials is a binomial distribution and is given by:

p(x) = [tex]nC_{x} p^{n-x} q^{x}[/tex]

Here, n = 6

x = 2

p = probability of one head = [tex]\frac{1}{2}[/tex]

q = 1 - p

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

= [tex]\frac{1}{2}[/tex]

Substitute these values, we get,

p(2) = [tex]6C_{2} (\frac{1}{2} )^{6-2} (\frac{1}{2} )^{2}[/tex]

= [tex]15(\frac{1}{2} )^{6}[/tex]

= [tex]\frac{15}{64}[/tex]

= 0.234

= 23.4%

We know that [tex]6C_{2} =6C_{6-2}[/tex]

[tex]6C_{2} =6C_{4}[/tex]

Now,

p(4) = [tex]6C_{4} (\frac{1}{2} )^{6-4} (\frac{1}{2} )^{4}[/tex]

= [tex]15(\frac{1}{2} )^{6}[/tex]

= p(2)

Hence, the theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Answer:

W >_2/7

Step-by-step explanation:

Answer:

Total number of ice cream cones sold =  15x +7

Step-by-step explanation:

Given the statement: Suppose 8x + 16 ice cream cones were sold on Saturday and 7x - 9 were sold on Sunday.

⇒ Ice cream cones were sold on Saturday = 8x+16

and

Ice cream cones were sold on Sunday = 7x -9

We have to find the total number of ice cream cones sold.

Total number of ice cream sold = Ice cream cones sold on Saturday + Ice cream sold on Sunday

Substitute the given values we get;

Total number of ice cream sold = [tex]8x + 16 + 7x -9 = 15x + 7[/tex]

Therefore, the total number of ice cream cones sold is, 15x +7

Answer:

0.8

Step-by-step explanation:

Answer:

0.8

Step-by-step explanation:

Answer:

diagonal^2 = side^2 + side^2

144*10 = 2s^2

144*5 = s^2  

side = 12sqrt(5) f

Step-by-step explanation:

Answer:

c = 5 and t = 20

Step-by-step explanation:

t = 2c + 10, t = 4c

so

2c + 10 = 4c

-2c = -10

c = 5

t = 4(5)

t = 20

Answer:

c=5 t=20

Step-by-step explanation:

Answer:

The correct answer option is dependent.

Step-by-step explanation:

We are given the following two equations and we are to determine whether these are independent, dependent or inconsistent:

[tex]y = 3x + 6[/tex] --- (1)

[tex]6x - 2y = -12[/tex] --- (2)

To compare these equations with each other, it is a good idea to write them in the same format with y being the subject. So rearranging equation (2) to get:

6x - 2y = -12

6x + 12 = 2y

2y = 6x + 12

y = 3x + 6

A system of equations is said to be dependent when the same line is written in two different forms so that there are infinite solutions.

Hence, this system of equations is dependent having infinite solutions.

The system of equations are classified as independent

To classify the system of equations as independent, dependent, or inconsistent, we can analyze their coefficients.

The given system of equations is:

y = 3x + 6

6x - 2y = -12

Comparing the coefficients, we can see that the slopes of the equations are equal (-2/-6 )

Reduce the fraction to smaller forms, we get;

1/3

Now, since the slopes are different, the system is consistent and has a unique solution, indicating an independent system.

Thus, the equations are independent.

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Answer:

Option C is correct.

[tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]

Step-by-step explanation:

Given the expression:  [tex]\sum_{i=1}^{18} (7i^2+9)[/tex]

Using properties of summation:

Using properties of summation in the given expression we have;

[tex]\sum_{i=1}^{18} (7i^2+9)[/tex]

= [tex]\sum_{i=1}^{18} 7i^2 + \sum_{i=1}^{18} 9[/tex]

=[tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]

Therefore, the following given expression uses the properties of summation to represents is, [tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]

Answer:

B

Step-by-step explanation:

solving the inequality

9 - y > 12 ( subtract 9 from both sides )

- y > 3 ( multiply both sides by - 1 )

Remembering to reverse the inequality symbol when multiplying/ dividing by a negative quantity

y < - 3 ← reverse symbol

Thus y is less than or equal to - 3

The only value from the list which makes this true is - 6 → B

To find a solution to the inequality 9 – y > 12, one must first simplify the inequality to y < -3. After comparing all the options, the correct answer is Option B (– 6), as it is the only value that is less than -3.

The question asks to find a value of y that satisfies the inequality 9 – y > 12.

To find the solution, we need to isolate y on one side of the inequality:

Now that we have the solution to the inequality, we can evaluate the given options.

Therefore, the correct answer is Option B: – 6, because – 6 < – 3.

Alright, so we are given a triangle where all the angles are the same. Now - we need to write a proof that when IE bisects KM, it creates equal angles.

Given:

IKM is equiangular

IE is perpendicular to KM

This is enough to prove that IKE is congruent to IME because:

IEK and IEM are both 90 degrees, since IE is perpendicular to KM

KIE and MIE are the same degree measure, since I is being bisected.

This leaves us with only one angle remaining, and since we already know that the first two angles are congruent to their counterpart - we also know that IKE is congruent to IME because all interior angles of triangles add up to 180°, and we know the other two angle sets to be congruent.

Answer:

Step-by-step explanation:

(y+6)=(1/2)x

Answer:

To determine if fractions are equivalent, you need to get a common denominator.  When the denominators are the same, if the numerators are the same, the fractions are equivalent

Step-by-step explanation:

To determine if fractions are equivalent, you need to get a common denominator.  When the denominators are the same, if the numerators are the same, the fractions are equivalent

There is only one unique triangle that can be drawn with side lengths of 4cm, 5cm, and 10cm.

A triangle is defined by its side lengths. In order for a triangle to be formed, the sum of any two side lengths must be greater than the third side length. In this case, we have side lengths of 4cm, 5cm, and 10cm. We can check if these lengths can form a triangle by checking the triangle inequality:

Since all three inequalities are true, a triangle can be formed with side lengths of 4cm, 5cm, and 10cm. Therefore, there is only one unique triangle that can be drawn with these side lengths.

Answer:

(x - 5i)(x + 5i)

Step-by-step explanation:

Find the roots by solving x² + 25 = 0

hence x² = - 25 ( take the square root of both sides )

x = ± 5i

x² + 25 = (x - 5i)(x + 5i)

Answer: 11 girls were not selected.

Step-by-step explanation:

First let's find out how many girls their were in total. In this case their are 23.

Let's subtract 12 from 23. That ends up to be 11. (subtract 23 from 11 / 11 from 23)

-23

-12

-------

11

What we know:

- Twenty-three girls tried out for the cheerleading squad.

- Only 12 girls will be chosen for the team.

Answer and Explanation:

The answer is 11 because,

When trying to find out how many girl's that where not selected you just simply subttact 23 from 12.

23-12=11

That being said, the answer is 11.

Answer:

The correct option is 1.

Step-by-step explanation:

From the given table is notices that the function f(x) is a downward parabola.

The maximum value of f(x) is 5 at x=1.

The function g(x) is

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

vertex of the parabola is

[tex](\frac{-b}{2a}, g(\frac{-b}{2a}))[/tex]

[tex](\frac{-4}{2\times 1}, g(\frac{-4}{2\times 1})[/tex]

[tex](2, g(2))[/tex]

Put x=2.

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

Therefore the vertex of g(x) is (2,4). The vertex of a downward parabola is the maximum point of the function.

Therefore ƒ(x) has the greater maximum. Option 1 is correct.

Answer:

ƒ( x) has the greater maximum.

Step-by-step explanation:

The first step is to calculate the difference between the original selling price and the sale price. Then divide the markdown amount by the original selling price and multiply by 100 to find the percent markdown.

The first step in finding the percent markdown is to calculate the difference between the original selling price and the sale price. Subtract the sale price from the original selling price to find the markdown amount. Then, divide the markdown amount by the original selling price and multiply by 100 to find the percent markdown.

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The percent markdown is approximately 14.99%.

The first step in finding the percent markdown is to calculate the difference between the original selling price and the sale price.

In this case, the difference is $175.80 - $149.42 = $26.38.

Next, divide the difference by the original selling price and multiply by 100 to find the percent markdown.

So, $26.38 / $175.80 × 100 = 14.99%.

Therefore, the percent markdown is approximately 14.99%.

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Answer:

1x^2 - 4x is the quotient and remainder is 7

Step-by-step explanation:

Let use synthetic division

First we write all the coefficients of x^3 - 5x^2 + 4x + 7 inside

we need to divide by x-1. x-1=0 so x= 1

so we put 1 outside

The coefficients of x^3 - 5x^2 + 4x + 7  is 1, -5, 4, 7

    1                       1            -5           4            7

                                            1             -4         0

                 -------------------------------------------------------------

                            1              -4             0         7

Here 7 is the remainder

Now we write the answer in descending powers of x

1  -4  and 0 we have

The highest exponent in the question is x^3

when we divide by x-1 then highest exponent becomes x^2

So answer is 1x^2 - 4x + 0 that is 1x^2 - 4x

Answer:

x^2 - 4x + (7) x - 1

Step-by-step explanation:

This is correct Hope this Helps! :)