Michael and Tom are brothers. Their combined age is 20, and Tom is 4 years older than Michael. What are Michael and Tom’s ages?

Answer:

C

Step-by-step explanation:

If there is an expression such as:

[tex]\frac{A*B}{A*C}[/tex]

we can cancel out A from top and bottom and that will leave us with [tex]\frac{B}{C}[/tex]

Note: Let A, B, C, be any algebraic expression

For the problem given, we can simply cut (x+1) from top and bottom by rules of algebra. So the remaining terms are:

[tex]\frac{(x-1)}{(x+7)}[/tex]

This is option C

Answer:

C)

Step-by-step explanation:

When you have a*b/c*a, a crosses out, simplifying to b/c:

(x+1)(x-1)/

(x+1)(x+7)

When "crossing out", you are really just simplifying it to 1/1:

1*(x-1)/

1*(x+7)

Which is the same as:

(x-1)/(x+7)

Therefore, C is the correct answer

Given the functions

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

Function (a)

f(-x) = (-x)³ + 5(-x)² + (-x)  

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

The function is neither even nor odd.

Function (b)

f(-x) = (-x)² + (-x)

       = -(-x² + x)

The function is neither even nor odd.

Function (c)

f(-x) = -(-x)  

      = x

      = -f(x)

Because f(-x) = -f(x) the function is odd.

Answer: f(x) = -x is an odd function.

The correct equation representing the situation where Nancy's mother added candies to the 16 candies already in the bag is 16 + c = 32. Subtracting 16 from both sides gives the result c = 16, which is the number of candies her mother added.

The subject of this question is mathematics and it belongs to the middle school level. Nancy began with 16 candies and ended up with 32 candies after her mother added some. Nancy wants to find out how many candies her mother added.

To solve this problem, we need to use a simple addition equation. The equation that correctly represents the situation is 16 + c = 32. This equation says that Nancy's original amount of candies (16) plus the candies her mother added (c) equals the new total amount of candies (32).

To solve for c (the number of candies her mother added), we simply subtract 16 from both sides of the equation. Therefore, c = 32 - 16, which leads to c = 16, which is the number of candies her mom put in the bag.

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Final answer:

The correct equation for Nancy's chocolate candies is 16 + c = 32, solving for c reveals that 16 candies were added. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.

Explanation:

The question asks to identify the correct equation to solve for the number of chocolate candies, c, that Nancy's mom put in the bag. Nancy originally had 16 chocolate candies, and her mother added some candies to the bag, increasing the total to 32 candies. The equation that represents this situation is 16 + c = 32. This equation can help Nancy find out how many candies her mother added to the bag.

To solve for c, we need to perform a subtraction operation:

This calculation gives us the number of candies Nancy's mother added, which means c = 16 candies.

Jenny's Chocolate Question

If Jenny has some chocolates, eats two, and gives half of what is left to Lisa, resulting in Lisa having six chocolates, then we must work backward to find the initial amount. Since Lisa received half of the remainder, Jenny must have had 12 chocolates after eating two. This means Jenny started with 14 chocolates as:

The correct answer for Jenny's beginning number of chocolates is 14.

Answer:

[tex]\boxed{\text{3.0 T}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}M + T + W + Th + F & = & \text{Total}\\2.4 + 4.4 + 1.8 + 2.8 + F & = & 14.4\\11.4 + F & = & 14.4\\F & = & 3.0\\\end{array}\\\text{Friday's sales of chlorine were }\boxed{\textbf{3.0 T}}[/tex]

Answer: There are 3 tons of chlorine sold on Friday.

Step-by-step explanation:

Since we have given that

Number of tone of chlorine on Monday = 2.4

Number of tone of chlorine on Tuesday = 4.4

Number of tone of chlorine on Wednesday = 1.8

Number of tone of chlorine on Thursday = 2.8

Total number of week's sales = 14.4 tons

So, we need to find the number of tone of chlorine on Friday.

According to question we get that

[tex]14.4=2.4+4.4+1.8+2.8+x\\\\14.4=11.4+x\\\\x=14.4-11.4\\\\x=3[/tex]

Hence, there are 3 tons of chlorine sold on Friday.

Answer:

case 1) 972 in³

case 2) 1,458 in³

Step-by-step explanation:

Remember that

1 ft=12 in

case 1)

If the dimensions of the crate are

9 in x 9 in x 1 ft

Convert to inches

9 in x 9 in x 12 in

The volume is equal to

V=9*9*12=972 in³

case 2)

If the dimensions of the crate are

9 in x 9 in x 1 1/2 ft

Convert to inches

9 in x 9 in x (12*1.5) in

9 in x 9 in x 18 in

The volume is equal to

V=9*9*18=1,458 in³

Answer:

121.5

Step-by-step explanation:

9x9x1.5=121.5

C' ( 0, 3)

A' ( 2 , 1)

C'A' = CA

C'A' = √(2^2 + 2^2) = √8 = 2√2

C'A' = CA = 2√2

The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.

We have,

The coordinates of point A =(2, 1)  and C = (-2, 2)

Now,

To find the distance between two points, (x₁, y₁) and (x₂, y₂), we can use the distance formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given the points (2, 1) and (-2, 2), we can substitute the values into the formula:

Distance = √[(-2 - 2)² + (2 - 1)²]

Distance = √[(-4)² + 1²]

Distance = √[16 + 1]

Distance = √17

Therefore,

The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.

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Answer:

Multiply [tex] \frac { 3 } { 4 } [/tex] by 8.

Step-by-step explanation:

We are given the following expression and we are to find its quotient:

[tex] \frac { 3 } { 4 } [/tex] ÷ [tex] \frac { 1 } { 8 } [/tex]

This can also be written as:

[tex]\frac{\frac{3}{4}}{\frac{1}{8} }[/tex]

Since the two fractions are being divided so to change this division sign into a multiplication sign, we will take the reciprocal of the fraction in the denominator and multiply 3/4 by 8.

[tex]\frac{3}{4} \times 8[/tex] = 6

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {3} {4}} {\frac {1} {8}} =[/tex]

Applying double C we have:

[tex]\frac {3 * 8} {4 * 1} =\\\frac {24} {4}[/tex]

This is equivalent to the following expression:

[tex]\frac {3} {4} * 8 = \frac {24} {4}[/tex]

Answer:

Option B

Answer:

Step-by-step explanation:

[tex]h(x)=x-7,\ g(x)=x^2\\\\(g\circ h)(x)=g\bigg(h(x)\bigg)-\text{exchange x to x - 7 in}\ g(x):\\\\(g\circ h)(x)=(x-7)^2\\\\(g\circ h)(5)-\text{put x = 5 to the equation}\\\\(g\circ h)(5)=(5-7)^2[/tex]

Answer:

3 1/2 ; 3 19/20 ; 3 39/40

Step-by-step explanation:

Find common denominators. Change all mixed fraction to improper fractions before finding common denominators.

3 1/2  = 6/2 + 1/2 = 7/2

3 19/20 = 60/20 + 19/20 = 79/20

3 39/40 = 120/40 + 39/40 = 159/40

Find the common denominators. The smallest common denominators is 40. Remember that what you do to the denominator you do to the numerator:

3 1/2 = (7/2)(20/20) = 140/40

3 19/20 = (79/20)(2/2) = 158/40

3 39/40 = (159/40) = 159/40

Least to Greatest:

3 1/2 ; 3 19/20 ; 3 39/40

~

Answer:

B 48

Step-by-step explanation:

it is b I know because I got it correct

Answer:

Its b

Step-by-step explanation:

You have to estimate the numbers so b is the best answer

Answer:

$1,475

Step-by-step explanation:

times 100 by 14 which is 1400

but then add 75 onto that

Answer:

$1475

Step-by-step explanation:

One week costs $100.

Note that:

The $75 enrollment fee is a one-time payment.

$100 per week is the amount that is paid per week, and can change depending on the amount of week they pay for.

In this case, the child would be there for 14 weeks. Set the equation. Let x = amount of weeks, and t = total cost:

100x + 75 = t

We know that the child will be there for 14 weeks, so plug in 14 for x.

(100)(14) + 75 = t

t = (100 * 14) + 75

Simplify. Remember to follow PEMDAS. Multiply first, then add:

t = (1400) + 75

t = 1475

The total cost for 14 weeks is $1475.

~

Answer:

41.03 square feet

Step-by-step explanation:

The area of a sector is given by the formula:

[tex]A=\frac{1}{2}r^2\theta[/tex]

Where A is the area, r is the radius and [tex]\theta[/tex] is the angle in radians.

Given the values, we plug into the formula and solve:

[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(5.6)^2(\frac{5\pi}{6})\\A=41.03[/tex]

Answer:

48 sq. units

Step-by-step explanation:

The area of a trapezoid is given by half sum of the bases multiplied by the height

[tex]=\frac{1}{2} (a+b)h[/tex]

where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid

But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae  is covered by the median

[tex]Median=\frac{1}{2} (a+b)[/tex]

Hence area, A, of a trapezoid is simplified to product of median and amplitude

[tex]A=amplitude*median\\\\A=6*8=48sq.units[/tex]

Answer:

=48 sq. units.

Step-by-step explanation:

Area of a trapezoid =h× (a+b)/2

(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.

Median=8 inches

Altitude is the distance between the two parallel sides= 6 inches

A=6 inches×8 inches

=48 sq. units.

Answer:

V looking graph

(absolute value function)

Step-by-step explanation:

We are looking for a relation that passes the vertical line test.

Basically if you can play a vertical line on your graph and it touches more than once on that vertical line (your graph) then it isn't a function.

The only one that is a function here is the V looking graph.

The graph in the shape of a V (absolute value function)

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Answer:

29/12

Step-by-step explanation:

In an isosceles triangle, two sides are equal.

Therefore:

25/6+25/6+u = 10 3/4

50/6+u=43/4

u=43/4-50/6

u=43/4-25/3

u=129/12-100/12

u=29/12

Answer:

Where   is the figure????

Step-by-step explanation:

Answer:

Step-by-step explanation:

A horizontal line has an equation: y = a  (a - any real number).

Each point on a horizontal line y = a, has coordinates (x, a)    (x - any real number).

We have the point (-7, 5) → y = 5

Answer:bsdaosdfhaodsifhaosdfaidfhaoif

have a nice time reading and understanding his:)

Step-by-step explanation:

considering APB as the triangle

AP is the tangent to the circle.

∴ OA ⊥ AP  (Radius is perpendicular to the tangent at the point of contact)

⇒ ∠OAP = 90º  

In Δ OAP,

sin ∠OPA = OA/OP = r/2r [Diameter of the circle]

∴ sin ∠OPA = 1/2 = sin 30º

⇒ ∠OPA =  30º

Similarly, it can he prayed that ∠OPB = 30

How, LAB = LOP + LOB = 30° + 30° = 60°  

In APB,  

PA = PB [lengths &tangents drawn from an external point to circle areequal]  

⇒ ∠PAB = ∠PBA --- (1) [Equal sides have equal angles apposite to them]  

∠PAB + ∠PBA + ∠APB = 180° [Angle sum property]  

∠PAB + ∠PBA + ∠APB = 180° - 60° [Using (1)]  

⇒ 2∠PAB = 120°

⇒ ∠PAB = 60°  

From (1) and (2)  

∠PAB = ∠PBA = ∠APB = 60°

APB is an equilateral triangle.

Answer:

200

Step-by-step explanation:

8x^2 + 80x = −5

Factor out an 8

8(x^2 + 10x) = −5

Take the coefficient of the x term, divide by 2 and then square it

10/2 = 5, 5^2=25

Remember we have the 8 outside, so we are multiplying by 8

8*25 =200

Add 200 to each side

8(x^2 + 10x + 25) = −5 + 200

Answer:

Missing number is 200.

Step-by-step explanation:

In the completing the square method we follow the following steps,

Step 1 : Move constant term to the right side,

Step 2 : Make 1 as the coefficient of [tex]x^2[/tex]

Step 3 : Add square of the half of the coefficient of x in the left side and balance the equation,

Here, the given equation,

[tex]8x^2+ 80x = -5[/tex]

[tex]8(x^2 + 10x) = -5[/tex]

∵ coefficient of x = 10,

Half of 10 = 5,

Square of 5 = 25,

Thus, we need 25 inside the bracket in left side,

For this, add 200 on both side,

[tex]8(x^2 + 10x+25) = -5+200[/tex]

Hence, missing number in the last step is 200.

Answer:

it would be D

Step-by-step explanation:

Answer:

The number line D)

Step-by-step explanation:

Carly withdraws $18 from her bank account.

We assume that Carly has $x in her account. She withdraws $18 from her bank account.

So we have to subtract $18 from $x amount.

Which is $x - 18.

So we are subtracting $18 from her account.

It should be represented by an integer -18.

Now we have to identify the which number line represents -18.

It is D)

Answer:

Part 1)  shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]  

Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]

Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]

Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]

see the attached figure

Step-by-step explanation:

Part 1) we have

[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]  

Multiply by -10 both sides

[tex]x-2 \leq 6[/tex]

Adds 2 both sides

[tex]x \leq 6+2[/tex]

[tex]x \leq 8[/tex]

The solution is the interval -----> (-∞,8]

All real numbers less than or equal to 8

In a number line the solution is the shaded area at left of x=8 (close circle)

Part 2) we have

[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]

Multiply by -6 both sides

[tex]100x+11 \leq -489[/tex]

Subtract 11 both sides

[tex]100x \leq -489-11[/tex]

[tex]100x \leq -500[/tex]

Divide by 100 both sides

[tex]x \leq -5[/tex]

The solution is the interval -----> (-∞,-5]

All real numbers less than or equal to -5

In a number line the solution is the shaded area at left of x=-5 (close circle)

Part 3) we have

[tex]\frac{3x}{2}+105 \leq 96[/tex]

Multiply by 2 both sides

[tex]3x+210 \leq 192[/tex]

Subtract 210 both sides

[tex]3x \leq 192-210[/tex]

[tex]3x \leq -18[/tex]

Divide by 3 both sides

[tex]x \leq -18/3[/tex]

[tex]x \leq -6[/tex]

The solution is the interval -----> (-∞,-6]

All real numbers less than or equal to -6

In a number line the solution is the shaded area at left of x=-6 (close circle)

Part 4) we have

[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]

Multiply by -18 both sides

[tex]13x-10 \leq 81[/tex]

Adds 10 both sides

[tex]13x \leq 91[/tex]

Divide by 13 both sides

[tex]x \leq 91/13[/tex]

[tex]x \leq 7[/tex]

The solution is the interval -----> (-∞,7]

All real numbers less than or equal to 7

In a number line the solution is the shaded area at left of x=7 (close circle)

Final answer:

The equation of a circle with center (2,7) and a radius of 5 is (x - 2)² + (y - 7)² = 25.

Explanation:

To find the equation of a circle with its center at (2,7) and a radius of 5, we use the standard form of the equation for a circle which is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

Plugging in the given values for our circle we have:

(x - 2)² + (y - 7)² = 5²

Expanding the right side of the equation gives us:

(x - 2)² + (y - 7)² = 25

This is the desired equation of the circle. It represents a circle with a radius of 5, centered at the point (2,7).

[tex]\bf \begin{cases} f(x) = x\\ g(x) = 2x+7 \end{cases}~\hspace{7em}g(x)=11\implies \stackrel{g(x)}{11}=2x+7 \\\\\\ 4=2x\implies \cfrac{4}{2}=x\implies \implies \boxed{2=x} \\\\[-0.35em] ~\dotfill\\\\ f[90x]\implies f\left[90\left( \boxed{2} \right)\right]\implies f(180)=\stackrel{x}{180}[/tex]

Answer:

5:5 (first box, pencils to pens)

7:3 (second box, coloured pencils to crayons)

The probability of picking a pen (1st box): 5/10

The probability of picking a crayon (2nd box): 3/10

Probability of picking both: 5/10*3/10 = 15/100

Step-by-step explanation:

Mass = Volume x density

Mass = 8.4 gm

Density = 2.4 g/cc

Substituting

       8.4 = Volume x 2.4

       Volume = 3.5 cm³

[tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3[/tex]

We need to find radius, r

Substituting volume value

              [tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3=3.5\\\\r^3=0.836\\\\r=0.941cm=1cm[/tex]

Radius of grape = 1 cm  

To solve the problem we must know about volume.

The radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.

The volume can be defined as the space occupied by the three-dimensional object.

It is given by the ratio of mass(m) and density(ρ).

[tex]\text{Volume of the object} = \dfrac{m}{\rho}[/tex]

Given to us

Mass of the object, m = 8.4 grams

Density of the object, ρ = 2 gram/cm³

As it is already mentioned that the volume is equal to the ratio of its mass to density. therefore,

[tex]\text{Volume of the object} = \dfrac{m}{\rho}\\\\\text{Volume of the object} = \dfrac{8.4}{2}\\\\\text{Volume of the object} = 4.2\ cm^3[/tex]

Thus, the volume of the object is 4.2 cm³.

To find the radius of the sphere we will use the formula of the volume of the sphere.

[tex]\text{Volume of sphere} = \dfrac{4}{3}\pi r ^3[/tex]

Substitute the values,

[tex]4.2 = \dfrac{4}{3}\pi r ^3\\\\r = 1\rm\ cm[/tex]

Hence, the radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.

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Answer:

x = 80, y = 140 and z = 20

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles in the triangle with x and equate to 180

x + 60 + 40 = 180

x + 100 = 180 ( subtract 100 from both sides )

x = 80

40° and y form a straight angle and are supplementary, hence

40 + y = 180 ( subtract 40 from both sides )

y = 140

Sum the 3 angles in the triangle with z and equate to 180

z + y + 20 = 180, that is

z + 140 + 20 = 180

z + 160 = 180 ( subtract 160 from both sides )

z = 20

Answer:

[tex]\sqrt[3]{x}[/tex]

Step-by-step explanation:

we have

[tex](x^{\frac{1}{15}})^{5}[/tex]

Simplify

Multiply the exponents

[tex](x^{\frac{1}{15}})^{5}=x^{\frac{1}{15}*5}=x^{\frac{5}{15}}=x^{\frac{1}{3}}=\sqrt[3]{x}[/tex]

Answer:

[tex]\sqrt[3]{x}[/tex].

Step-by-step explanation:

We have been given an expression [tex](x^{\frac{1}{15}})^5[/tex]. We are asked to simplify our given expression.

We will use power rule of exponents [tex](a^b)^c=a^{b\cdot c}[/tex] to simplify our given expression as:

[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{15}\times 5}[/tex]

[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}\times 1}[/tex]

[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}}[/tex]

Using fractional exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex], we can write our expression as:

[tex](x^{\frac{1}{15}})^5=\sqrt[3]{x}[/tex]

Therefore, the simplified form of our given expression would be [tex]\sqrt[3]{x}[/tex].

When evaluating the expression [tex]b^2c - 1[/tex] for b = -4 and c = 2, we calculate b squared as 16, multiply by c to get 32, and subtract 1 to obtain the answer 31.

To evaluate the expression b2c - 1 for b = -4 and c = 2, we need to follow the order of operations, often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we calculate b², which is (-4)² = 16.

Next, we multiply this result by c, which gives us 16 * 2 = 32.

Finally, we subtract 1 from this product, resulting in 32 - 1 = 31.

Therefore, the evaluated expression [tex]b^2c - 1[/tex] is 31 when b = -4 and c = 2.

Final answer:

The situation with a constant rate of change is the length of a bead necklace compared with the number of identical beads, as it represents a linear relationship with a constant slope.

Explanation:

The situation that is most likely to have a constant rate of change is option C, which describes the length of a bead necklace compared with the number of identical beads.

In this scenario, each bead added to the necklace increases its length by a consistent amount. This defines a linear relationship, where the rate of change, also known as the slope in a linear equation, remains constant.

For example, if one bead adds one centimeter to the necklace, then ten beads will add ten centimeters, indicating that the rate of change is one centimeter per bead.

This can be depicted graphically as a straight line when you plot the number of beads against the length of the necklace.

Answer:

In step 1, he substituted into the volume formula incorrectly.

Step-by-step explanation:

James calculated the height of a cylinder that has a volume of 324 cubic inches.

radius = 12 inches.

The formula for volume is = [tex]\pi r^{2} h[/tex]

So, James calculated wrongly by using the wrong formula.

The step 1 is wrong.

Answer:

In step 1, he substituted into the volume formula incorrectly.

Step-by-step explanation: