can you help me solve each compound inequality and graph it's solution? 2 and 4 please and thank you

He got $245 for his birthday

For this case we have,

3/4 of a bushel of apples -----------------------> $ 9

1 bushel of apples -------------------------------> x

From here the value of x is cleared, resulting in:

[tex]x =\frac{(1)(9)}{\frac{3}{4} } \\\\x = 12\\[/tex]

2/3 of a bushel of apples -----------------------> $ 9

1 bushel of apples -------------------------------> x

From here the value of x is cleared, resulting in:

[tex]x = \frac{(1)(9)}{\frac{2}{3} }\\\\x = 13.50 \\[/tex]

Therefore it is convenient to buy apples in store 1 because it is cheaper.

Answer:

It is convenient to buy apples in store 1 because it is cheaper. A division must be made for each case because you want to find the unit cost of a product having the total cost and the amount in fraction.

2 and 1/10 of an hour

In other words, it is 2 hours and 6 minutes

Add 1/2 and 1 and 3/5 together to get 21/10

1. The rate of the boat in calm water is 50 miles per hour.

2. The rate of the current is 10 miles per hour.

How the rates are determined:

Let:

[tex]r_b[/tex] be the rate of the boat in calm water (in miles per hour).

[tex]r_c[/tex] be the rate of the current (in miles per hour).

Given:

With the current:

Distance: 120 miles

Time: 2 hours

Speed: [tex]r_b + r_c[/tex] (since the current aids the boat)

So, the equation is:

[tex]r_b + r_c = \frac{120}{2}[/tex] = 60 (Equation 1)

Against the current:

Distance: 120 miles

Time: 3 hours

Speed: [tex]r_b - r_c[/tex] (since the current opposes the boat)

So, the equation is:

[tex]r_b - r_c = \frac{120}{3}[/tex] = 40 (Equation 2)

Step 1: Solve the System of Equations

We have the system:

[tex]r_b + r_c = 60[/tex] (Equation 1)

[tex]r_b - r_c = 40[/tex] (Equation 2)

Step 2: Add the Two Equations

Adding Equation 1 and Equation 2:

[tex]r_b + r_c + r_b - r_c[/tex] = 60 +40

[tex]2r_b[/tex] = 100

[tex]r_b = 50[/tex] (Rate of the boat in calm water)

Step 3: Substitute [tex]r_b[/tex] into one of the Equations

Substitute [tex]r_b[/tex] =50 into Equation 1:

50+[tex]r_c[/tex] = 60

[tex]r_c[/tex] = 10 (Rate of the current)

Domain is (5, ∞), {x| x is greater than 5} for all integer n

Range is (-∞, ∞), {y| y belongs to Reals numbers}

[tex]F(x) = log (x - 5)[/tex]

Set up the equation for x

[tex]x - 5 > 0[/tex]

or,

x > 5

So the domain is all values of x greater than 5 to infinity.

Range is set of all correct or valid values of y.

Range = (-∞, ∞), {y| y belongs to Reals numbers}

Final answer:

To find the value of sin10° + tan40° × cos10°, calculate each trigonometric function separately, multiply tan40° by cos10°, then add sin10° to the product. The approximate result is 1.0005, but use a calculator for a precise value.

Explanation:

To solve the expression sin10° + tan40° × cos10°, we first need to calculate the individual trigonometric values. The cosine of 10 degrees (cos(10°)) is approximately 0.9848.

Next, we calculate the tangent of 40 degrees (tan(40°)). According to the provided data, tan(40°) is approximately 0.839.

Using the trigonometric identity for the sine of a sum of angles, we cannot directly simplify the expression because the addition and multiplication involve different angles. Therefore, we perform the multiplication first:

tan40° × cos10° = 0.839 × 0.9848 ≈ 0.8265

Next, we add the value of sine of 10 degrees (sin10°) to this result. Given that sin10° is approximately 0.174:

sin10° + (tan40° × cos10°) = 0.174 + 0.8265 ≈ 1.0005.

However, due to possible rounding in intermediate steps, the actual value might be slightly different when calculated using more precise values or a calculator set to the correct mode.

5x+7 is greater because 2(x-3)+4     =2x-2

Answer:

Okay Im going off of my work because we did some in class and then the rest by ourselves but i turned mine in yesterday but didnt recieve a grade yet but i hope these help you...

The number number line it is seven units apart.

The absolute value larger number smaller number would be 2 - (-5). So what you do with that is keep the 2 change the subtraction sign to plus sign and change the negative 5 to positive 5. So your answer would be 7.

And smaller number to larger number would be -5 - 2. And then you do the same steps as the last one. Keep the negative five, change the subtraction sign to addition sign and make the two  negative. And that answer would be -7

2. For the number two problem you would plot the robins nest just below the top of the verticle line. the red squirrel den would be right next to the zero but a tad up. And the groundhog burrow would be below the zero mark and a little before the end of the verticle line.

Next, for groundhog burrow to red squirrel den you put the number 0.3-(-1.2)=1.5    Red squirrel den to Robin’s nest 3.6 – 0.3 = 3.3. And for the last one Groundhog burrow to Robin’s nest 3.6 – (-1.2) = 4.8.

3. you have to turn the 1 1/2 and 3/4 into 8ths. 1/2= 3*4 = 12 and for the denominator 2*4 = 8. So 12/8.

The next one is 3*2 which is 6 and 4*2=8

so now you have 12/8, 6/8, and 1/8

you have to add the points on the chart (i cant really help you on this part because i do not know how to upload picture) but you would make 24 and then you find where 12/8 would go and draw the hops but on mine the hop looks like how you would draw a rainbow but just one for the 12. Then do the same for the 6 and add 1 for the last one to make 19.

On mine I add the 12 + 6 + 1 = 19 so that is how i got mine. (sry if this a bad explination)

it should kinda look like this on the chart.

| | | | | | | | | | | | | | | | | | | | | | | | they should be spaced apart like this.

and for the last one i put cup 3 because it bigger than the amount of ingrident in the recipe. (im not sure if that one was the answer this is the only part we didnt get help on in class)

Polygon FGHIJ is the result of the rotation of ABCDE. 

A = F ⇒ 117°

B = G ⇒ 90°

C = H ⇒ 127°

D = I ⇒ 90°

E = J ⇒ 117°

The measure of angle BCD remains the same because the rotation involves the whole polygon. Thus, it is still 127°

Read more on Brainly.com - https://brainly.com/question/1591791#readmore

Answer:

m∠ABC = 117 °

m∠BCD = 90 °

m∠DEA = 90°

m∠CDE = 127°

Step-by-step explanation:

Since this is a series of rigind transformations, the angles of the figure do not change, so:

A=F= 117°

B=G=117°

C=H=90°

D=I=127

E=J=90°

Step 1. Expand

-3x - 4 = 5x + 20

Step 2. Add 3x to both sides

-4 = 5x + 20 + 3x

Step 3. Simplify 5x + 20 + 3x to 8x + 20

-4 = 8x + 20

Step 4. Subtract 20 from both sides

-4 - 20 = 8x

Step 5. Simplify -4 - 20 to -24

-24 = 8x

Step 6. Divide both sides by 8

-24/8 = x

Step 7. Simplify 24/8 to 3

-3 = x

Step 8. Switch sides

x = -3

Answer:

2 6/7

Sorry if I'm wrong.

1/4 - [-3/8]

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

Negative times negative become positive

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

Now to add fractions we make the denominator same

4  and 8 are in the denominator

Least common denominator of 4  and 8 is 8

To make denominators same , we multiply the numerator and denominator of first fraction by 2.

[tex]\frac{1*2}{4*2} + \frac{3}{8}[/tex]

[tex]\frac{2}{8} + \frac{3}{8}[/tex]

The denominators are same so we combine the numerators

[tex]\frac{2+3}{8}[/tex]

[tex]\frac{5}{8}[/tex]

[tex]f(x)=4x-11\\\\\text{Put the value of x = 5 to the equation of the function}\\\\f(5)=4(5)-11=20-11=9[/tex]

15.97 as amixed fraction would be 15 97/100

Hope helps! -Aparri

The decimal number  15.97 as a mixed fraction is [tex]15\frac{97}{100}[/tex].

To write 15.97 as a mixed fraction, we need to express it as a whole number combined with a fraction.

The whole number part can be obtained by taking the integer part of 15.97, which is 15.

To determine the fraction part, we need to consider the decimal portion. Since 15.97 has two decimal places.

we can express it as a fraction with a denominator of 100 (since there are two decimal places).

The decimal portion, 0.97, can be written as 97/100.

Putting it together, 15.97 can be expressed as the mixed fraction:

15 + 97/100

Therefore, 15.97 as a mixed fraction is [tex]15\frac{97}{100}[/tex].

To learn more on Fractions click:

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Answer:

$112.50

Step-by-step explanation:

You take 25 + 25 +25 +25 = 100

that equals 8 pizzas

half of 25 is 12.5

so for one pizza it is $12.50

100 + 12.5 = 112.50

No, x^2 + 20x - 100 is not a perfect square trinomial.

No, x^2 + 20x - 100 is not a perfect square trinomial.

In order for a trinomial to be a perfect square, it must be in the form (a + b)^2 or (a - b)^2.

The given trinomial can be factored as (x + 10)(x - 10), which is not in the form of a perfect square.

Steps:

isolate " x "  for -2x + 2y  + 3z  = 0 ;    x = -  ( - 3z - 2y ) / 2

Subsititute : x = -  ( - 3z - 2y ) / 2

- 2 * (  - ( - 3z - 2y ) / 2 ) - y + z = - 3

2 * ( -  ( - 3z - 2y ) / 2 ) + 3y  + 3z  =5

isolate " z " for  :  - 2  ( -  ( - 3z - 2y ) / 2 ) - y+ z = - 3 ;  z = - ( - 3 +  3y / 2 )

subsititute  z = - ( - 3 + 3y / 2 ) :

2* ( - ( -3* ( - ( - 3 +3y / 2 ) - 2y / 2  ) + 3y  + 3  ( - ( - 3 + 3y / 2 ) = 5

isolate y for 2 ( -( - 3 ) - 3 + 3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5

y = 1

for z =  - ( - 3+ 3y ) / 2

subsititute y = 1

z = - ( - 3 + 3  * 1 ) / 2

z =  0

For x  = - ( - 3z - 2y ) / 2

subsititute y = 1

subsititute z = 0

x = -  ( - 3 *0 - 2 * 1 ) / 2

x =  1

x = 1  , y =  1  , z = 0

To solve the equation we have to rearrange the terms i.e. like terms on one side

[tex]-28 = 22 - 5x[/tex]

Subtracting 22 from both sides we get

[tex] -28 -22 = 22-5x - 22[/tex]

[tex] -50 = -5x[/tex]

Divide both sides by -5 we get

[tex]\frac{-50}{-5} = \frac{-5x}{-5}[/tex]

On simplifying we get

[tex] x =10[/tex]

Hence, x= 10 is your answer

Hope this will help

Answer:

6.875

Step-by-step explanation:

We have been given that after a storm Michael measured 6 7/8 inches of snow. We are asked to show this amount  as a decimal.

We can represent our improper fraction as a whole and a part as:

[tex]6\frac{7}{8}=6+\frac{7}{8}[/tex]

Let us convert [tex]\frac{7}{8}[/tex] as a decimal.

[tex]6+\frac{7}{8}=6+0.875=6.875[/tex]

Therefore, the amount as a decimal would be 6.875.

We are given

nine less than three times a number is forty

we know that

we always start our order of operation from left to right

This sentence represents equality

Let's assume that number as 'x'

Left side is :

3x-9

Right side is :

40

so, we can write as

[tex]3x-9=40[/tex].............Answer

( [72-60] / 72 )*100 =  50 / 3 = 16.7 %

Answer:

y = m(x - 2)

Step-by-step explanation:

If y over x-2= m and we want to solve for y, multiply both sides of the equation y over x-2= m by (x - 2) first, to remove fractions:

y = m(x - 2)

Final answer:

The total bill at Pepe's Pizza Palace was $16.60. Annie paid $6.53, Suz paid $3.32, and Cynthia paid the remaining $8.80.

Explanation:

To determine the total bill and how much each girl paid, we first acknowledge that Cynthia has stated she would pay the remaining $8.80. This gives us a starting point to figure out the portions of the bill that Annie and Suz will pay.

Suz suggests that Annie pays one-third of the bill and offers to pay $1 more than that amount. Suz is to pay 20% of the bill. If Cynthia pays the remaining amount, let's denote the total bill as B.

Using the information given:

Annie pays one-third of the bill plus $1: (1/3)B + $1

Suz pays 20% of the bill: 0.20B

Cynthia pays the remaining $8.80.

Add these up to get the total bill.

(1/3)B + $1 + 0.20B + $8.80 = B

Solving this equation:

0.33B + 0.20B + $8.80 - $1 = B - $1

0.53B + $7.80 = B

B - 0.53B = $7.80

0.47B = $7.80

Dividing both sides by 0.47:

B = 7.80 / 0.47

B = $16.60 (rounding to two decimal places)

Therefore, the total bill amounts to $16.60. Now to find out how much each girl pays:

Annie's portion:

(1/3)*16.60 + $1 = $5.53 + $1 = $6.53

Suz's portion:

0.20*16.60 = $3.32

Cynthia's portion is the amount she agreed to pay:

$8.80

To summarize, the total bill was $16.60. Annie paid $6.53, Suz paid $3.32, and Cynthia paid $8.80.