The length of a rectangle is 7 inches less than its width. The perimeter of the
rectangle is 54 inches. Find the length and the width of the rectangle. Explain your
reasoning.

-12. 2 negatives always make a positive

Answer:

See Explanation

Step-by-step explanation:

Given the illustration in the question

Required:

Use deductive reasoning to prove (a)

From your question, you need only the (b) part and this is done as follows;

Step 1: Represent the number with: n

Step 2: Multiply n by 4: 4n

Step 3: Add 10 to (2) above: 4n + 10

Step 4: Divide (3) above by 2: (4n + 10)/2 = 4n/2 + 10/2 = 2n + 5

Step 5: Subtract 5 from (4): 2n + 5 - 5 = n

Hence, the end result is proved to be 2n

Test this with any of the given illustration in (a) part, your answer will always be 2n

Answer:

84.85 feet or 60[tex]\sqrt2[/tex] feet.

Step-by-step explanation:

Given that:

Distance of paths between each pair of consecutive bases is 60 ft.

To find:

Distance that the ball needs to travel if it is thrown directly from home plate to second base?

Solution:

Actually the given problem can be mapped to a right angled triangle in which base and height are given to be equal to 60 ft (because each pair of consecutive bases are 60 ft apart), Plus, they are at right angles to each other.

So, kindly refer to the image attached.

AB and BC are the distance of paths between consecutive bases.

And we have to find AC.

We can use Pythagorean theorem to find out the Hypotenuse of the triangle.

According to Pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = AB^{2} + BC^{2} \\\Rightarrow AC^{2} = 60^{2} + 60^{2} \\\Rightarrow AC = \sqrt{2 \times 60^2}\\\Rightarrow AC = \bold{60\sqrt{2}\ ft = 84.85\ ft}[/tex]

Answer:

la respuesta es 25

Step-by-step explanation:

para calcular este tanto ciento, sugerimos usar esta formula:

%/100 = parte/total

realizando la multiplicatión en cruz:

25% x 100 = 100 x parte, o

2500 = 100 x parte

ahora es sólo dividir por 100 y obtener la respuesta:

parte = 2500/100 = 25

Answer:

1 ≤ x  < 4

Step-by-step explanation:

-2≤ 2x - 4 < 4

Add 4 to each side

-2+4 ≤ 2x - 4+4 < 4+4

2 ≤ 2x  < 8

Divide each side by 2

2/2 ≤ 2x/2  < 8/2

1 ≤ x  < 4

Answer:

a.0<=x<-2

Step-by-step explanation:

Answer:

0.972 is a rational real number.

Step-by-step explanation:

A rational number is defined as the number that can be expressed from the result of a fraction.

1/4 = 0.25

An integer number is all those that do not have a decimal part.

(-∞ ..., -3, -2, -1, 0, 1, 2, 3, ... ∞)

Natural numbers are all those positive numbers starting from 0 to infinity.

N = (0, 1, 2, 3, 4, 5, ... ∞)

Answer:

[tex]\bold{21.07^\circ}[/tex]

Step-by-step explanation:

The given values can be mapped to an isosceles [tex]\triangle ABC[/tex].

Side AB = AC

Vertical height, AD = 2.1 m

The distance between one side to the other side of ceiling = 10.9 m

To find:

Pitch (Angle of the roof ) = ?

i.e. [tex]\angle B[/tex] or [tex]\angle C[/tex] = ? (because it is isosceles triangle, so both will be equal)

Solution:

As [tex]\triangle ABC[/tex] is isosceles, so vertical height will divide the side BC in two equal parts

i.e. [tex]BD = DC = \frac{1}{2} BC[/tex]

[tex]\therefore BD = \frac{10.9}{2} = 5.45 m[/tex]

In [tex]\triangle ABD[/tex], let us use tangent trigonometric property.

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tanB = \dfrac{AD}{BD}\\\Rightarrow tanB = \dfrac{2.1}{5.45}\\\Rightarrow tanB = 0.385\\\Rightarrow \angle B = tan^{-1}( 0.385)\\\Rightarrow \bold{\angle B = 21.07^\circ}[/tex]

Answer:

You would get 2.25 back.

Step-by-step explanation:

1.50 + 2.00 + 3.25 + 1 = 7.75 Dollars

10 - 7.75 = 2.25

Answer:

66

Step-by-step explanation:

12+14=26

26+40=66

Answer:

a. and e.

Step-by-step explanation:

Hello, there are two ways to handle this kind of question.

... Either you solve the equation ...

[tex]x^2+4x-9=x+1\\\\x^2+3x-10=0\\\\x^2-2x+5x-10=x(x-2)+5(x-2)=(x+5)(x-2)=0\\\\x= -5 \ \ or \ \ x = 2[/tex]

So the right answers are a. and e.

... Or, you check which answer can be right.

We replace x by 2 and the two expressions are equal.

[tex]2^2+4*2-9=4+8-9=3 \ and \ 2+1=3[/tex]

So this is a. 2

We replace x by 4 and the two expressions are not equal.

[tex]4^2+4*4-9=16+16-9=23 \ and \ 4+1=5[/tex]

So this is not b. 4

We replace x by -7 and the two expressions are not equal.

[tex]7^2-4*7+9=49-28+9=30 \ and \ -7+1=-6[/tex]

So this is not c. -7

We replace x by -3 and the two expressions are not equal.

[tex]3^2-4*3-9=9-12-9=-12 \ and \ -3+1=-2[/tex]

So this is not d. -3

We replace x by -5 and the two expressions are equal.

[tex]5^2-4*5-9=25-20-9=-4 \ and \ -5+1=-4[/tex]

So this is e. -5

We replace x by -4 and the two expressions are not equal.

[tex]4^2-4*4-9=16-16-9=-9 \ and \ -4+1=-3[/tex]

So this is not f. -4

Thank you.

Answer:

The answer is 72 degrees

Step-by-step explanation:

I hope this helps, leave a heart and rating plz!!?:)

The correct option  is 72°. The measure of angle CBE is 72° by using the data angle ABC is (3 x) degrees and angle DEF is (2 x) degrees.

To determine the measure of angle CBE, we need to analyze the given information. We are provided with the angles ABC and DEF, where angle ABC is represented by 3x degrees and angle DEF is represented by 2x degrees.

From the description, we can see that angle CBE is formed by the combination of angles ABC and DEF. The angle ABC is adjacent to angle CBE at point B, and the angle DEF is adjacent to angle CBE at point E.

To find the measure of angle CBE, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle ABC and angle D E F are adjacent to angle CBE and form a straight line, they are supplementary angles. Therefore, the sum of angle ABC and angle DEF is 180 degrees.

We can set up the equation:

3x + 2x = 180°

Combining like terms, we get:

5x = 180°

To solve for x, we divide both sides of the equation by 5:

x = 36°

Now that we know the value of x, we can find the measure of angle CBE by substituting x into the expression for angle DEF:

2x = 2 * 36 = 72 degrees

Therefore, the measure of angle CBE is 72 degrees.

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Answer & Step-by-step explanation:

The Segment Addition Postulate states that AB + BC = AC when C is between A and B.

The segment addition postulate states that if point C is between points A and B then the segment AB will be equal to the sum of AC and CB.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the segment addition postulate states that if point C is between points A and B.

The expression for the line segment can be formed mathematically as below:-

AB = AC + CB

From the above equation, it is observed that the sum of the segment AC and CB will be equal to AB.

Therefore, according to the segment addition postulate, segment AB will equal the sum of the segments AC and CB if point C is located between points A and B.

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Answer:

3/5

Step-by-step explanation:

A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

[tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex]

Given the conic equation   [tex]r=\frac{3}{5-3cos(\theta)}[/tex]

We have to make the conic equation to be in the form [tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex].

[tex]r=\frac{3}{5-3cos(\theta)}\\\\Multiply\ the\ numerator\ and \ denominator\ by \ 1/5\\r=\frac{3*\frac{1}{5} }{(5-3cos(\theta))*\frac{1}{5}}\\\\r=\frac{3*\frac{1}{5} }{5*\frac{1}{5}-3cos(\theta)*\frac{1}{5}}\\\\r=\frac{\frac{3}{5} }{1-\frac{3}{5}cos(\theta)}[/tex]

Comparing with  [tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex]. gives:

e = 3/5, p = 1

The eccentricity is 3/5

Answer:

jklfhgugt

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Why is f(x)=(3x+1/3)^2+8/9 not the vertex form of f(x)=9x^2+2x+1?

A.The expression has a constant outside of the squared term.

B. The expression is not the product of two binomials.

C. The variable x has a coefficient.

D. Some of the terms are fractions instead of integers.

Vertex form is a(x -h)^2 +k. The coefficient of x inside parentheses is 1. The given form is not vertex form because the leading coefficient has not been removed to outside parentheses.

__

2) What is the vertex of the parabola with the equation y=(x−2)^2+10?

A. (−2, −10)

B. (2, 10)

C. (−2, 10)

D. (2, −10)

Vertex form is a(x -h)^2 +k. Comparing to the given equation, we find the vertex (h, k) = (2, 10).

__

3) For the given function, identify the x- and y-intercepts if any, the vertex, the axis of symmetry, and the maximum or minimum value. f(x)=−x^2+25

A. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,−25). The vertex is (0,−25). The axis of symmetry is x=0. The minimum value of the function is −25.

B. There are no x-intercepts. The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is y=0. The maximum value of the function is 25.

C. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.

D. The x-intercepts are (−25,0) and (25,0). The y-intercept is (0,5). The vertex is (0,5). The axis of symmetry is x=0. The maximum value of the function is 5.

The x-intercepts are the values of x that make y=0. They are (±5, 0). The y-intercept is the value of y when x=0. It is (0, 25).

__

4) A student says that the function f(x)=−x^2−9 has the x-intercepts (−3,0) and (3,0). Is the student correct? If not, explain why.

A. The student is correct.

B. The student is not correct. The equation f(x)=0 has one real solution, so the x-intercept is (9,0).

C. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph has only one x-intercept, (0,0).

D. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph does not have any x-intercepts.

The parabola opens downward and has a maximum value of -9, so cannot cross the x-axis. There are no x-intercepts, hence no real solutions.

Answer:

the answer is 15

Step-by-step explanation:

f(x)=5(2-x)

f(-1)=5(2-(-1))

f(-1)=5(2+1)

f(-1)=5(3)

f(-1)=15

Answer:

[tex] x^9[/tex]

Step-by-step explanation:

[tex] \huge {x}^{2} . {x}^{7} = {x}^{2 + 7} = {x}^{9} \\ [/tex]

Answer:

6

Step-by-step explanation:

If the graph intersects the x-axis, then there is an x-intercept at that point. So, we know that 3 and 9 are the x-intercepts of the parabola.

Parabolas can only have 0, 1, or 2, x intercepts. The x coordinate of the vertex will be the average of the x coordinates of the x-intercepts, since the vertex will be in the middle of the 2 x intercept points.

Take the average of 3 and 9:

(3 + 9) / 2

12 / 2

= 6

The x coordinate of the vertex is 6.

Answer:

Step-by-step explanation:

[tex]LHS = \frac{1}{m^{2}}-\frac{1}{m^{2}+1}\\\\\\=\frac{1*(m^{2}+1)}{m^{2}*(m^{2}+1)}-\frac{1*m^{2}}{(m^{2}+1)*m^{2}}\\\\\\=\frac{m^{2}+1- m^{2}}{(m^{2}+1)*m^{2}}\\\\\\=\frac{1}{(m^{2}+1)m^{2}}=RHS[/tex]

Answer:

Q1)i) Q= 7p

ii) Q= 35

iii) P= 6

Q2)x= 3

Q3) B=4

Answer:

c = - [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

The product of the zeros = [tex]\frac{c}{a}[/tex] = [tex]\frac{1}{2}[/tex]

Given

2x² - 3x - 5c

with a = 2 and c = - 5c , then

[tex]\frac{-5c}{2}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

- 10c = 2 ( divide both sides by - 10 )

c = [tex]\frac{2}{-10}[/tex] = - [tex]\frac{1}{5}[/tex]

Answer:

48

Step-by-step explanation:

180 - 90 - 42 = x

x = 48

Answer:

A) 48°

Step-by-step explanation:

Sum of all angles of a triangle = 180

90 + 42 + x = 180

Add like terms

132 +x = 180

Subtract 132 form both sides

x = 180 -132

x = 48°

Is it a true or false? If yes, the answer is false

If u have to solve the answer will be hx=x.2+kx=x-hk2

Answer:

SA= 289.56 m^2

Step-by-step explanation:

Answer:

Median

Step-by-step explanation:

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Hope this helps! Please tell me if I did anything wrong, thank you and have a great day!

Answer:+c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given , x = 7

let's find :

[tex] \sf{5 - 3(x - 1)}[/tex]

Plug the value of x

⇒[tex] \sf{5 - 3(7 - 1)}[/tex]

Subtract 1 from 7

⇒[tex] \sf{5 - 3 \times 6}[/tex]

Multiply the numbers

⇒[tex] \sf{5 - 18}[/tex]

Calculate

⇒[tex] \sf{ - 13}[/tex]

Hope I helped!

Best regards!!

The value of 5-3(x-1) when x=7 is -13.

Evaluation is nothing but to solve an algebraic expression means to find the value of an expression by replacing the value of the variable in it.

To evaluate the expression value, we simply substitute the variable from its given value and simplify the expression by using order of operations.  

In our case, the given expression is:

5-3(x-1)

Substitute the given number i.e., 7 for the variable in the expression:

5-3(7-1)

Solve the bracket first:

5-3(6)

Now solve the multiplication part:

5 - 18

Finally Subtract 5 from -18, we get:

-13

Hence the final value of the expression is -13 at x=7.

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Quilt

Step-by-step explanation: