Grandma says Baby Bertha (BB) should get $1000 at birth plus $50 per year. Grandpa disagrees; he thinks BB should get $1000 at birth plus an additional 4% of the accumulated amount each year. Grandma and Grandpa will continue to contribute additional funds into the account as long as BB doesn’t make a withdrawal. Which option should BB’s parents select? Why?

Step-by-step explanation:

The polynomial 1 - bx - x + b can be factored by rearranging the terms to (1 + b) - x(1 + b), allowing us to factor out 1 + b, resulting in the factored form (1 + b)(1 - x).

The polynomial in question, 1 \\u2212 bx \\u2212 x + b, can be factored by rearranging and grouping terms. Indeed, the suggestion to factor out at least one x from all terms that contain it can be helpful in some cases, for example, ax^2+bx+c. However, for the polynomial given, we need to rearrange the terms to (1 + b) \\u2212 x(1 + b). Notice that 1 + b can be factored out, resulting in (1 + b)(1 \\u2212 x).

Therefore, the factored form of 1 \\u2212 bx \\u2212 x + b is (1 + b)(1 \\u2212 x).

In general, when factoring polynomials, being attentive to common factors and rearranging terms to identify them can lead to a simpler expression. For a quadratic equation like ax^2+bx+c=0, factoring is a powerful tool, often applied after identifying an integrating factor or using the quadratic formula.

Answer:

(6,-7)

(2,1)

(-4,13)

Step-by-step explanation:

we have

[tex]2x+y=5[/tex] -----> equation A

[tex]3y=15-6x[/tex] ----> equation B

Multiply the equation A by 3 both sides

[tex]3(2x+y)=3(5)[/tex]

[tex]6x+3y=15[/tex]

isolate the variable 3y

[tex]3y=15-6x[/tex] -----> equation C

equation B and equation C are equal

That means -----> is the same line

so

The system has infinity solutions

Remember that

If a ordered pair is a solution of the line, then the ordered pair must satisfy the equation of the line

Verify each ordered pair

1) (6,-7)

substitute the value of x and the value of y in the linear equation

[tex]3(-7)=15-6(6)[/tex]

[tex]-21=-21[/tex] ---> is true

so

The ordered pair is a solution of the system of equations

2) (2,1)

substitute the value of x and the value of y in the linear equation

[tex]3(1)=15-6(2)[/tex]

[tex]3=3[/tex] ---> is true

so

The ordered pair is a solution of the system of equations

3) (-2,-9)

substitute the value of x and the value of y in the linear equation

[tex]3(-9)=15-6(-2)[/tex]

[tex]-27=27[/tex] ---> is not true

so

The ordered pair is not a solution of the system of equations

4) (-4,13)

substitute the value of x and the value of y in the linear equation

[tex]3(13)=15-6(-4)[/tex]

[tex]39=39[/tex] ---> is true

so

The ordered pair is a solution of the system of equations

Answer:

(6,-7)

(2,1)

(-4,13)

Step-by-step explanation:

got it right on edg2020 :)

Answer:

68in

Step-by-step explanation:

Divide the area by 2 because a= l x w and squares sides are all the same.

To find the approximate side length of a square game board with an area of 136in^2, you can use the formula for the area of a square and take the square root of the given area. The approximate side length is 11.66 inches.

To find the approximate side length of a square game board with an area of 136in2, we can use the formula for the area of a square, which is length * length. In this case, we need to find the square root of 136 to get the side length. The square root of 136 is approximately  11.66 inches.

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Answer:

a- 16/100

b- 1/6

c- not sure

Step-by-step explanation:

[tex]\large\text{Hey there!}[/tex]

[tex]\mathsf{The\ sphere\ formula\ is: \dfrac{4}{3}\pi\times r^3}[/tex]

[tex]\mathsf{Now, that\ we\ have\ our\ formula\ let's\ solve\ for\ the\ equation}[/tex]

[tex]\mathsf{So,\ first\ \bf{\underline{DIVIDE}}}\mathsf{\ both\ of\ your\ sides\ by\ \pi}[/tex]

[tex]\mathsf{\dfrac{4}{3}r^3=972}\\\\\rightarrow\ \mathsf{r^3=972\times\dfrac{3}{4}}\\\\\mathsf{972\times\dfrac{3}{4}=729}\\\\\mathsf{\rightarrow\ r^3=729}[/tex]

[tex]\mathsf{\sqrt[\mathsf{3}]{\mathsf{729}} = 81}\\\\\mathsf{\sqrt{81}=81\div9=9}\\\\\mathsf{\sqrt{81}=9}\\\\\mathsf{r=9}[/tex]

[tex]\boxed{\boxed{\mathsf{\bf{Answer: \boxed{\mathsf{radius = \bf{9}}}}}}}\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Answer: The products of corresponding x- and y- values of an inverse variation function are constant.

As x increases, y also increases.

The product of coordinate pairs are not equal: (165) (198) = 32,670 and (170) (204) = 34,680.

Step-by-step explanation:

Answer: They will travel about 131.18 yards.

Step-by-step explanation:

Given : A football field is 120 yards long by 53 yards wide.

We know that a football field is rectangular in shape.

Each interior angle in a rectangle is a right angle.

Then, by Pythagoras theorem, we have

(Diagonal)² = (Length)² + (Width)²

If a player runs diagonally from one corner to the opposite corner, then the length of the diagonal is given by :-

[tex](\text{Diagonal})=\sqrt{(120)^2+(53)^2}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{14400+2809}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{17209}\\\\\Rightarrow\ (\text{Diagonal})=131.183078177\approx131.18\text{ yards}[/tex]

Hence, they will travel about 131.18 yards.

Final answer:

The distance a player would travel running diagonally across a football field that is 120 yards long and 53 yards wide is approximately 131.183 yards.

Explanation:

The student asked about the distance a player would travel if they ran diagonally from one corner to the opposite corner of a football field that is 120 yards long and 53 yards wide.

To solve this, we need to apply the Pythagorean theorem in which the length and width of the football field will be the legs of the right triangle and the diagonal the player runs will be the hypotenuse.

The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.

Therefore, the calculation will be as follows:

(120 yd)² + (53 yd)² = c².

Simplifying,

14400 yd² + 2809 yd² = c².

Adding these together gives us 17209 yd², and taking the square root of that gives us the length of the diagonal, which is the distance the player will travel.

Thus, c = √17209 yd2 ≈ 131.183 yards.

Answer:

96 units^2

Step-by-step explanation:

Base: 6 × 6 = 36

Faces: 5 × 6 = 30 (×2 = 60)

Add: 36 + 60 = 96

Answer:

96 units^2

Step-by-step explanation:

The Base: 6 × 6 = 36

The Faces: 5 × 6 = 30 (×2 = 60)

Then Add: 36 + 60 = 96

Hope to help.

Answer:

27/7.

Step-by-step explanation:

(f/g)x = (7 + 4x) / 7

(f/g)(5) = (7 + 4(5)/ 7

= 27/7.

Yo sup??

f(x)=7+4x

g(x)=7

f/g(5)

=7+4*5/7

=27/7

Hope this helps

B. False

There are cases where this is not true, but if you want to prove that, you'll need to know what f and g are. For example, if f(x) = x - 3 and g(x) = x2, then f(g(x)) is not equal to g(f(x)) because

f(g(x)) = x2 - 3 and g(f(x)) = (x - 3)2. Those 2 functions are not the same because f(g(0)) = -3 ≠ 9 = g(f(0)).

Function rules by equations | Algebra functions that match 1 variable to the other in a 2-variable equation. Functions are written using function notation. Create functions that match 1 variable to the another in a 2-variable equation.

there are Some Examples of Functions

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The absolute error is 2 feet and percent error is 18.18%

Step-by-step explanation:

Given,

Estimated length = 13 feet

Actual length = 11 feet

Absolute error = Estimated length - Actual length

Absolute error = 11 - 13 = -2 feet

Absolute error = 2 feet

Percent error = [tex]\frac{Absolute\ error}{Exact\ value}*100[/tex]

Percent error = [tex]\frac{2}{11}*100[/tex]

Percent error = [tex]\frac{200}{11}=18.18 \%[/tex]

The absolute error is 2 feet and percent error is 18.18%

The absolute error is 2 feet and the percent error is approximately 18.2%

The absolute error in Deon's estimate can be found by subtracting the actual value from the estimated value and taking the absolute value. So that's |13 - 11| which equals 2 feet.

The percent error can be found by dividing the absolute error by the actual value and then multiplying by 100 to convert it into a percentage. That's (2 / 11) * 100 which equals approximately 18.2%. If we round to the nearest tenth, we get 18.2%.

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Answer:

Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.

Step-by-step explanation:

to find the distance between two point A(-4, -2) and B(-7, -7) we use the following distance formula

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

x1=-4, x2=-7

y1=-2, y2=-7

so,

[tex]d=\sqrt{(-7-(-4))^2+(-7-(-2) )^2\\}\\\\d=\sqrt{(-7+4)^2+(-7+2)^2 }\\\\d=\sqrt{(-3)^2+(-5)^2 }\\\\\\\\d=\sqrt{9+25}\\ \\d=\sqrt{34}[/tex]

Answer:

Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.

Explanation:

I got it right,

Hope this Helps!

Answer:

106 gal

Step-by-step explanation:

step 1

Find the area of the path

we know that

The area of the path is given by the formula

[tex]A=\pi r_2^{2} -\pi r_1^{2}[/tex]

[tex]A=\pi [r_2^{2} -r_1^{2}][/tex]

where

r_2 is the radius of the pool plus the width of the path

r_1 is the radius of the pool

we have

[tex]r_1=22/2=11\ yd[/tex] ---> the radius is half the diameter

[tex]r_2=11+6=17\ yd[/tex]

substitute

[tex]A=\pi [17^{2}-11^{2}][/tex]

[tex]A=168\pi\ yd^2[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]A=168(3.14)=527.52\ yd^2[/tex]

step 2

Find the gallons of coating needed

Divide the area of the path by 5

so

[tex]527.52/5=105.5\ gal[/tex]

Round up

therefore

106 gal

To calculate how many gallons of coating are needed, we find the area of the path by subtracting the area of the pool from the total area covered. This equals to 527.52 yd². As each gallon of coating covers 5 yd², we need 105.504 gallons. However, since the paint is sold in whole gallons, we round it up to 106 gallons.

To determine how many gallons of coating are needed, we first need to calculate the area of the ring-shaped path around the pool.

The pool is a circle with a diameter of 22 yd, so its radius is 11 yd. The path is around this pool and has a width of 6 yd. Therefore, the outer radius of the path is 11yd (radius of pool) + 6yd (width of path)=17 yd. The area of a circle is given by the formula πr² where r is the radius and π is a constant, approximately equal to 3.14.

So, the area of the outer circle is 3.14 × (17 yd)² = 907.46 square yards, and the area of the inner circle (pool) is 3.14× (11 yd)² = 379.94 square yards. The area of the path is the difference of those two areas, 907.46 yd² - 379.94 yd² = 527.52 yd².

Since one gallon of the coating can cover 5 sq yd, the number of gallons required is the total area divided by the area that one gallon can cover, which is 527.52 yd² / 5 yd²/gallon = 105.504 gallons. Since paint comes in whole gallons, you'll need to round up to the next whole number, which is 106 gallons.

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The largest radius for the swimming pool is 15.1 feet

Step-by-step explanation:

Step 1:

Circumference of the circular swimming pool built by Dan  = 95 feet

We need to determine the largest radius for the pool.

Step 2 :

Circle's circumference  is given by 2πr

Where r represents the radius

This shows that the radius is in direct proportion to the circumference. Hence the radius corresponding to the maximum circumference will be the largest possible radius

So we have 2πr = 95

=> r = [tex]\frac{95}{2\pi }[/tex]  

=> r =   [tex]\frac{95}{2}[/tex] × [tex]\frac{7}{22 }[/tex]  where [tex]\pi = \frac{22}{7}[/tex]

=> r = 15.1 feet (rounded off to tenth of a foot)

Step 3 :

The largest radius for the swimming pool is 15.1 feet

Final answer:

the largest radius possible for the pool, to ensure the circumference does not exceed 95 feet, is 15.1 feet.

Explanation:

Calculating the Largest Radius for a Swimming Pool

To find the largest possible radius for Dan's circular swimming pool with a circumference of no more than 95 feet, we will use the formula for the circumference of a circle, which is C = 2πr.

We need to solve for r (radius) when C ≤ 95 feet.

Setting up the equation:

Therefore, the largest radius possible for the pool, to ensure the circumference does not exceed 95 feet, is 15.1 feet.

Addition property of equality

Division property of equality

Solution:

Given inequality is:

3x - 2 > 4

[tex]\mathrm{Add\:}2\mathrm{\:to\:both\:sides}[/tex]

Here, Addition property of equality is used

When the same amount is added to both sides of an inequality, then the inequality is still true

3x - 2 + 2 > 4 + 2

3x > 6

[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]

Here, Division property of equality is used

When we divide both sides of an equation by the same nonzero number, the sides remain equal.

[tex]\frac{3x}{3}>\frac{6}{3}\\\\x > 2[/tex]

Thus the property used in each step of solving the inequality is found

Answer:

Step-by-step explanation:

56.3% of the student got A

15 students got A

Then,

Let the total number of students be x

56.3% of x= got A

56.3/100 × x =15

0.563x=15

Then x=15/0.563

x=26.6

The number of students can't or be 26.6 so let approximate it

Then, x=27

Therefore 27students are in the class

Step-by-step explanation:

Since, x=8 and x=-5 are the roots.

Therefore, (x - 8) & (x - 5) will be factors.

Hence, required quadratic equation can be given as:

[tex](x - 8)(x - 5) =0 \\ \\ \therefore {x}^{2} + ( - 8 - 5) x+ ( - 8) \times ( - 5) = 0 \\ \\ \therefore {x}^{2} + ( - 13) x+ 40= 0 \\ \\ \huge \red{ \boxed{ \therefore {x}^{2} - 13x+ 40= 0 }} \\ is \: the \: required \: quadratic \: equation.[/tex]

Answer:

[tex]minor\ arc\ BD=100^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

A circumscribed angle is the angle made by two intersecting tangent lines to a circle

so

In this problem

BC and CD are tangents to the circle

BC=CD ----> by the Two Tangent Theorem

That means

Triangle ABC and Triangle ADC are congruent

so

[tex]m\angle BAC=m\angle DAC[/tex]

Find the measure of angle BAC

In the right triangle ABC

[tex]m\angle BAC+m\angle BCA=90^o[/tex]

substitute given value

[tex]m\angle BAC+40^o=90^o[/tex]

[tex]m\angle BAC=90^o-40^o=50^o[/tex]

Find the measure of angle BAD

[tex]m\angle BAD=2m\angle BAC[/tex]

[tex]m\angle BAD=2(50^o)=100^o[/tex]

Find the measure of minor arc BD

we know that

[tex]minor\ arc\ BD=m\angle BAD[/tex] -----> by central angle

therefore

[tex]minor\ arc\ BD=100^o[/tex]

Final answer:

The measure of the minor arc BD is d. 80°, because it is twice the measure of the inscribed angle BCA, which is 40°.

Explanation:

When we are looking for the measure of a minor arc in a circle, and we know the measure of the inscribed angle that subtends that arc, we can find the measure of the arc by understanding that the inscribed angle is half the measure of the arc it cuts from the circle. Given that angle BCA measures 40°, and assuming BCD is an inscribed angle that subtends the arc BD, we can deduce that the minor arc BD is actually twice the measure of the inscribed angle BCA.

Therefore, to find the measure of minor arc BD, we double the measure of angle BCA:

Measure of minor arc BD = 2 × measure of angle BCA
Measure of minor arc BD = 2 × 40°
Measure of minor arc BD = 80° (d.)

To find the number that 37.5% of it equals 6, set up an equivalent fractions equation, cross-multiply, and solve for the unknown number. In this case, 37.5% of 16 is 6.

The question pertains to finding a certain number when given a percentage of that number. Here, we're asked to find the number of which '37.5% is 6'. We can solve this through simple arithmetic and the use of equivalent fractions. An important rule to remember is that 'percentage' literally means 'per 100', so 37.5% can be written as the fraction 37.5/100.

To find the unknown number (let's call it X), you can set up the equation 37.5/100 = 6/x, where 'x' is the number we're trying to find. Then you cross-multiply to solve for 'x': 37.5 * X = 6 * 100. Simplifying this, X = (6 * 100) / 37.5. Calculating that out gives X = 16. Therefore, 37.5% of 16 is 6.

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The value of the unknown number whose 37.5 percent equals 6 is 16.

Given the parameter:

37.5% of what number is 6

The problem is asking for 37.5% of some unknown number which gives 6.

We can represent the unknown number as x.

Now, the equation to find the unknown number will be:

37.5% of x = 6

Replace 37.5% with 37.5/100:

37.5/100 of x = 6

37.5/100 × x = 6

Solve for x:

0.375 × x = 6

0.375x = 6

Divide both sides by 6:

x = 6/0.375

x = 16

Therefore, the value of the number is 16.

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Answer:

There were 36 space rocks in total.

Step-by-step explanation:

if you see the number the line is divided into 6 or to get from 0 to 1 or 2 to 3 it takes 6 space that means the fraction should n/6.

n= a number

2 5/6 that means that there is 2 wholes or 2 6/6

6/6= 1

it is easy to plot 2 5/6 because it is already 5/6, you plot it right on the line that is before 3 or 5 spaces after 2.

1 2/3 is the same as 1 4/6

there is 1 whole or one 6/6. now it is easy you plot it on the line that is 4 spaces away from 1.

Plotted the points on the line. Please see attached.

2 5/6 = 17/6 = 2.83

1 2/3 = 5/3 = 1.67

Answer:   D) (x + 3)² + (y + 5)²  = 16

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²    

where (h, k) = center   and    r = radius

Given: (h, k) = (-3, -5)  r = 4

Equation: (x - (-3))² + (y - (-5))² = 4²

                 (x + 3)²  +  (y + 5)²  = 16

Answer:

Step-by-step explanation:

An obtuse triangle must contain an obtuse angle and two acute angles. An equilateral triangle must be 60 degrees in every corner, and thus there are 2+ acute angles. An isosceles triangle can have two angles that are 30 degrees (thus two acute), and a 120 degree angle

Work Shown:

i = P*r*t

157.50 = 2250*r*7 ... plug in given values

157.50 = 2250*7*r

157.50 = 15750r

15750r = 157.50

r = 157.50/15750 ... divide both sides by 15750

r = 0.01

The interest rate is 1%

To go from 0.01 to 1%, you move the decimal point 2 spots to the right.

Alternatively, you would multiply by 100.

Answer:7%

Step-by-step explanation:

The slope-intercept form is [tex]y=\frac{1}{2} x+5[/tex].

Solution:

Given data:

Slope of the line, m = [tex]\frac{1}{2}[/tex].

Point on the line = (–2, 4)

Here [tex]x_1=-2, y_1=4[/tex]

Let us find the slope-intercept form of the line using point-slope formula.

Point-slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]$y-4=\frac{1}{2} (x-(-2))[/tex]

[tex]$y-4=\frac{1}{2} (x+2)[/tex]

[tex]$y-4=\frac{1}{2} x+1[/tex]

Add 4 on both sides of the equation.

[tex]$y=\frac{1}{2} x+5[/tex]

Hence the slope-intercept form is [tex]y=\frac{1}{2} x+5[/tex].

Answer:

[tex] {12}^{ - 11} [/tex]

Step-by-step explanation:

The expression to be simplified is

[tex] {12}^{ - 6} \times {12}^{ - 5} [/tex]

We can see that the expression involves the idea of indices.Thus,we need to consider one of the laws of indices when dealing with the expression.

One of the laws of indices states that,

[tex] {a}^{m} \times{a}^{n} = {a}^{m + n} [/tex]

This means that when multiplying indices and the bases are equal, you repeat one of the bases and add the exponents.

This implies that

[tex] {12}^{ - 6} \times {12}^{ - 5} = {12}^{ (- 6 - 5)} [/tex]

Simplifying the exponent we obtain

[tex] = {12}^{ - 11} [/tex]

Answer:

15

Step-by-step explanation:

To isolate the variable, subtract 95 on both sides.

110=m + 95

m=15

Hope this helped! :)

Answer:

m=15

Step-by-step explanation:

110=m+95

Just subtract 95 from each side to isolate m and get your answer

110=m+95

-95     -95

15=m

Answer:

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

Step-by-step explanation:

step 1

Find the equation of the blue line

take the points

(0,-1) and (8,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5+1}{8-0}[/tex]

[tex]m=\frac{6}{8}[/tex]

simplify

[tex]m=\frac{3}{4}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=\frac{3}{4}[/tex]

[tex]b=-1[/tex] ---> see the graph

substitute the given values

[tex]y=\frac{3}{4}-1[/tex]

step 2

Find the equation of the black line

take the points

(0,9) and (3,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5-9}{3-0}[/tex]

[tex]m=-\frac{4}{3}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-\frac{4}{3}[/tex]

[tex]b=9[/tex] ---> see the graph

substitute the given values

[tex]y=-\frac{4}{3}+9[/tex]

therefore

The system of equations is

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

The equations of the blue and black lines are y = 3/4x - 1 and y = -4/3x + 9, respectively, based on their respective slopes and given points.

To find the equations of the blue and black lines, we start by determining their slopes using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on each line.

For the blue line:

Points: (0, -1) and (8, 5)

m = (5 - (-1)) / (8 - 0) = 6/8 = 3/4

Now, using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute the slope m = 3/4 and the given point (0, -1):

y = 3/4x - 1

For the black line:

Points: (0, 9) and (3, 5)

m = (5 - 9) / (3 - 0) = -4/3

Substituting the slope m = -4/3 and the given point (0, 9) into the slope-intercept form, we get:

y = -4/3x + 9

Therefore, the system of equations representing the blue and black lines is:

y = 3/4x - 1

y = -4/3x + 9

The question probable may be:

Write  system of equations could be used to solve for the point of intersection of the lines on the graph?