The length of a rectangle measures 5/8 of a foot. The width of the rectangle measures 2 1/2 feet. What is the area of the rectangle?

1) Let L = the larger # and S = the smaller #.

A large # is 5 more than twice a smaller #.....This gives Eq 1) L = 5 + 2S

Their sum is 80...This gives Eq 2) L + S = 80.

Substitute Eq 1) into Eq 2), you get

L + S = 80

5 + 2S + S = 80

3S = 75

S = 75 / 3 = 25

L = 5 + 2S

  = 5 + 2(25)

= 5 + 50

 = 55

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2) [-7,2)

- Vocabulary

· Interval

A set of values between two endpoints.

· Inequality

A mathematical expression which shows that two quantites are not equal.

Answer:

1) x = 25

2) 2(25)+5 = 55

-12<= x < 6

x <2 and x <= -7

Step-by-step explanation:

1) x

2) 2x + 5

x + 2x + 5 = 80

3x = 80 - 5

x = 75/3

x = 25

-24 <= 2x - 10

-24+10 <= 2x

-14/2 <= x

-7 <= x

2x -10< -6

2x < - 6 + 10

x < 4/2

x < 2

Answer:

angle 4 is the alternate angle

Answer: (A) angle 1

Step-by-step explanation:

[tex] \sf \underline{ \red{Solution - }} \\ [/tex]

Given,

[tex] \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\ [/tex]

The denominator is √11 - √5.

We know that

Rationalising factor of √a-√b is √a+√b.

Therefore, the rationalising factor of √11-√5 is √11+√5.

On rationalising the denominator them

[tex] \longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Multiplying (√11 + √5) with both the numerator of the fraction.

[tex] \longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\ [/tex]

Writing the squares of the numbers in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\ [/tex]

Performing subtraction in the denominator.

[tex] \longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\ [/tex]

Hence, the denominator is rationalised.

Answer:

1. A

2. C

Step-by-step explanation:

I could be wrong, that's my best guess. Im so sorry if im wrong, have a good day

Answer:

A trinomial is an algebraic equation composed of three terms and is normally of the form a[tex]x^{2}[/tex] + bx + c = 0, where a, b and c are numerical coefficients. The number “a” is called the leading coefficient and is not equal to zero (a≠0). For instance, x² − 4x + 7 and 3x + 4xy – 5y are examples of trinomials.

Step-by-step explanation:

Please recheck your question.

Answer:

1/3

Step-by-step explanation:

because 1/3 is 0.333333

Since only one box contains gold, then the gold must be in Box 2.

Let's analyze the statements in each box:

Box 1 says, "The gold is not in Box 2." If this statement is true, it means the gold cannot be in Box 2.

Box 2 says, "The gold is in this box." If this statement is true, it means the gold must be in Box 2.

Box 3 says, "The gold is not in this box." If this statement is true, it means the gold cannot be in Box 3.

Now, let's consider the possibilities:

If Box 1 is true, then the gold is not in Box 2 (as stated in Box 1), and it is also not in Box 3 (since Box 3 would be false, and only one box contains the gold).

As per Box's 1 statement, the gold is not in Box 2.

If Box 3 is true, then the gold is not in Box 3 (as stated in Box 3), and it is also not in Box 2 (since Box 2 would be false, and only one box contains the gold).

Therefore, the gold must be in Box 1.

To learn more about the puzzle tests;

https://brainly.com/question/28681162

#SPJ3

Answer:

-4 - 8-=-4

Step-by-step explanation:

Answer:

x= -1/23

Step-by-step explanation:

10

3.3×10= 33

Hope this helped you- have a good day bro cya)

Answer:

Step-by-step explanation:

Multiply the number of containers by the amount in each to find the total amount of sugar:

Answer:

The square route of 15 is irrational

Answer:

FH is the smallest side.

Step-by-step explanation:

This is called the relation between angles and sides where the smallest angle will have the smallest side opposite one another.

That means if measure G is the smallest then FH is the smallest side as FH is the opposite of measure G.

You can also say GH is the biggest or largest side since GH is opposite of measure F and measure F has the biggest angle.

So, FH is the smallest.

Answer:

2

Step-by-step explanation:

(4/3)^10 * (3/4)^6

Here lefts (4/3)^4

Answer:

0.2

Step-by-step explanation:

Answer:

8/9

Step-by-step explanation:

[tex]m = \frac{10 - 2}{10 - 1} = \frac{8}{9} [/tex]

Answer: 5/8 of a teaspoon of salt

Step-by-step explanation:

half of 1 is 1/2 or 4/8

half of 1/4 is 1/8

4/8 + 1/8 = 5/8

Answer:

1.3

2.6

3.24

Step-by-step explanation:

Hope it helps

Answer:

A = 4; B = -1 ; C = -29

Step-by-step explanation:

y = 4(x + 6) + 5

y = 4x + 24 +5

y = 4x + 29

Standard form: Ax + By = C

 4x - y = -29  

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

O {(1, 3), (2, 10), (6, 24), (24, 6

Answer:

30%

Step-by-step explanation:

2000-----100%

1400------x%

x=(1400×100)÷2000

X=70%

final we go 100%-70%=30%

Television price reduced for 30%

Hello!

y-y1=m(x-x1)

y-2=2(x-(-8)

y-2=2(x+8)

And that's our equation in point-slope form. Hope this helps!

~Just a joyful teen

[tex]SilentNature\\(GraceRosalia)[/tex]

Parallel lines have the same slope, while perpendicular lines have an opposite reciprocal slope.

Line 1:

-5y = 3x + 7

y = -3/5x - 7/5

Line 2:

y = -5/3x + 8

Line 3:

6x - 10y = -4

-10y = -6x - 4

y = 3/5x + 2/5

Line 1 and Line 2 are neither perpendicular nor parallel. While their slopes are reciprocals of each other, the signs are not opposite (both are negative).

Line 1 and Line 3 are neither perpendicular nor parallel. While the slope itself is the same, the signs are different.

Line 2 and Line 3 are perpendicular. Their slopes are opposite reciprocals of each other.

Hope this helps!! :)

Using the normal approximation to the binomial, it is found that there is a 0.0015 = 0.15% probability that at most 80 of these people will choose the creamery's brand.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The mean and the standard deviation are given by:

[tex]\mu = np = 300(0.35) = 105[/tex]

[tex]\sigma = \sqrt{np(1-p)} = \sqrt{300(0.35)(0.65)} = 8.26[/tex]

Using continuity correction, the probability that at most 80 of these people will choose the creamery's brand is [tex]P(X \leq 80 + 0.5) = P(X \leq 80.5)[/tex], which is the p-value of Z when X = 80.5, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80.5 - 105}{8.26}[/tex]

[tex]Z = -2.97[/tex]

[tex]Z = -2.97[/tex] has a p-value of 0.0015.

0.0015 = 0.15% probability that at most 80 of these people will choose the creamery's brand.

A similar problem is given at https://brainly.com/question/25298431

The lowest point of the cables above the bridge is 48 feet above the bridge.

The statement give us a parabola equation in standard form, the vertical distance of the lowest point above the bridge is determined by the y-coordinate of the vertex. Hence, the lowest point of the cables above the bridge is 48 feet above the bridge.

We kindly invite to check this question on parabolae: https://brainly.com/question/8495869

Answer:

7/10 - 3/7 - 1/5

Step-by-step explanation:

3/7-7/10-1/5

Step-by-step explanation:

Step-by-step explanation:

5/9×3/10= 15/90 simplification is 1/6

the correct is 1/6

Answer:

The 4th answer is correct

Step-by-step explanation:

[tex]\frac{5}{9} *\frac{3}{10} \\\\[/tex]

[tex]\frac{5*3}{9*10}[/tex]

[tex]\frac{15}{90}[/tex]

Now you can make the answer as the simplest form divide both sides by 15

[tex]\frac{15}{90} =\frac{1}{6}[/tex]

ANSWER IS,

[tex]\frac{1}{6}[/tex]

Hope this helps you.

Let me know if you have any other questions :-)