A bakery packages 868 cupcakes into 31 boxes. The same number of cupcakes are pput into each box. How many cupcakes are in each box?

Answer:

[tex]h=\frac{25}{b+r}[/tex]

Step-by-step explanation:

Given equation,

[tex]bh+hr=25[/tex]

For solving this equation for h,

We need to isolate h in the left side of the equation,

We can write,

[tex]h(b+r) = 25[/tex]    ( by the converse of distributive property ),

Divide both sides by b + r,

[tex]h=\frac{25}{b+r}[/tex]

Which is the required equation.

Answer:

c

Step-by-step explanation:

Answer:  The required scale factor that is used for the dilation is 3.

Step-by-step explanation:  Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.

We are to find the scale factor that is used for the dilation.

We know that

the scale factor of dilation is defined as

[tex]S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.[/tex]

From the graph, we see that

in rectangle ABCD, the length the side AB is 2 units

and

the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.

Therefore, the scale factor of dilation is given by

[tex]S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.[/tex]

Thus, the required scale factor that is used for the dilation is 3.

To solve the equation 9|9-8x|=2x+3, follow these steps: remove the absolute value by considering both positive and negative cases, combine like terms, solve for x, and simplify the solutions.

To solve the equation 9|9-8x|=2x+3, we need to isolate the variable x. Let's start by removing the absolute value by considering both positive and negative cases.

Case 1: Positive

9-8x = 2x+3

Combine like terms: -8x - 2x = 3 - 9

-10x = -6

Divide both sides by -10: x = -6/-10

Simplify: x = 0.6

Case 2: Negative

-(9-8x) = 2x+3

Distribute the negative sign: -9+8x = 2x+3

Combine like terms: 8x - 2x = 3 + 9

6x = 12

Divide both sides by 6: x = 12/6

Simplify: x = 2

Therefore, the solutions to the equation are x = 0.6 and x = 2.

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When cosθ >0 then , b² + c² > a².

" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."

Formula used

As per Cosine Rule

For a given ΔABC,

cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]

According to the question,

cosθ >0

⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0

⇒ b² + c² >a²

Hence, we conclude that Option D is correct.

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To solve the system by substitution, substitute the value of z in the equations and solve them simultaneously.

To solve the system by substitution, we need to substitute the value of z in the other equations. Given that z=5, we can substitute this value in the first and third equations:

2x - y + 5 = -4

-2x + 3y - 5 = 10

Now, we can solve these two equations simultaneously to find the values of x and y.

To solve a system of equations by substitution, express one variable in terms of the other and substitute it into the other equations to eliminate that variable before solving for the remaining variables.

To solve this system of equations by substitution:

By following these steps, you can find the values of x, y, and z that satisfy the system of equations.

Answer:

line HJ

Step-by-step explanation:

we know that

The equation of the line that has a slope of [tex]3[/tex] and a y-intercept at [tex](0, 0)[/tex] is equal to

[tex]y=3x[/tex] -----> is a proportional relationship

Remember that

If two lines are parallel , then their slopes are the same

Find the slope of the line HJ

[tex]H(-1,-4), J(1,2)[/tex]

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

[tex]m=\frac{2+4}{1+1}[/tex]

[tex]m=\frac{6}{2}[/tex]

[tex]m=3[/tex]

therefore

The line HJ is parallel to the line [tex]y=3x[/tex]

None of the given points is the solution to the inequality y < -|x|.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given inequality,

y < -|x|

As per the given below, the dotted line is not included in the region thus, point (1,-1) is not included.

Hence "None of the given points is the solution to the inequality y < -|x|".

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Answer:

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

Step-by-step explanation:

If Jolinda scored 21 points of 28 total, the fraction is:

[tex]\frac{21}{28}=\frac{3}{4}= 0.75(or75\%)[/tex]

Remember that a fraction is the representation of a portion among the total.

In addition, this fraction also would represent the effectiveness of Jolinda, we could say that she is able to score a 75% of team's points.

Answer:

Hmmm... interesting on my final I answered B: a=14, b=8 and got it wrong but, when I did it again I got C: a=17, b=6

Step-by-step explanation

Answer:

The value of a=17 cm and b=6 cm

C is correct option.

Step-by-step explanation:

Given: FGHJ is a kite.

Kite has property their adjacent sides are equal. Top two side of the kite is equal and bottom two side of the kite is equal.

FG=GH because ∠F=∠H.

30=2a-4

2a=34

a=17 cm

Similarly, ∠F=∠H

FJ=HJ

3b+6=24

3b=18

b=6 cm

Hence, The value of a=17 cm and b=6 cm

The correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]. Therefore the correct option is 2.

The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:

[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

For a square pyramid, the base area is given by [tex]\( \text{Base Area} = \text{side length}^2 \)[/tex].

In this case, the side length is [tex]\( x \)[/tex] and the height is [tex]\( y \)[/tex]. Therefore, the expression for the volume [tex]\( V \)[/tex] is:

[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

Now, let's compare this with the given options:

1. [tex]\( \frac{1}{3}xy \)[/tex] cm³

2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³

3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³

4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³

Now, we can see that the correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3}x^2y \, \text{cm}^3 \][/tex]

So, the correct option is option 2: [tex]\( \frac{1}{3}x^2y \)[/tex] cm³.

The correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]

Complete question:

A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?

1. [tex]\( \frac{1}{3}xy \)[/tex] cm³

2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³

3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³

4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³

Answer-

[tex]\boxed{\boxed{y^{\circ}=26^{\circ}\ 45'}}[/tex]

Solution-

As the triangle ABC is an isosceles triangle, with AC = BC.

So the angles A and B will be same, i.e

[tex]\Rightarrow \angle A=\angle B[/tex]

[tex]\Rightarrow 34^{\circ}=(x-5)^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=34^{\circ}+5^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=39^{\circ}[/tex]

As sum of all angles in a triangle is 180°, so

[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]\Rightarrow 34^{\circ}+39^{\circ}+4y^{\circ}=180^{\circ}[/tex]

[tex]\Rightarrow 4y^{\circ}=180^{\circ}-34^{\circ}-39^{\circ}[/tex]

[tex]\Rightarrow 4y^{\circ}=107^{\circ}[/tex]

[tex]\Rightarrow y^{\circ}=\dfrac{107^{\circ}}{4}[/tex]

[tex]\Rightarrow y^{\circ}=26.75^{\circ}[/tex]

[tex]\Rightarrow y^{\circ}=26^{\circ}\ 45'[/tex]

ratio is 5:4

5+4 =9

54 pounds divided by 9 = 6

6*5 = 30

6*4 = 24

Sam gets 30 pounds Bethan gets 24 pounds

Answer: Certain

Step-by-step explanation:

A probability is from 0 - 1, if not 0 or 1 it is a fraction, percentage, or decimal. 100% also equal to 1 is the highest amount you can get, therefore the answer is certain.