A shrub in Pam's back yard is about 1 3\8 feet tall. A small tree in her back yard is about 7 times as the shurd. About how tall is the tree

Final answer:

Greg's unit rate is  [tex]1\frac{5}{7}[/tex]  walls per hour, which is found by dividing 1/7 of a wall by 1/12 of an hour. The correct answer is option C: [tex]1\frac{5}{7}[/tex].

Explanation:

If Greg can build 1/7 of a brick wall in 1/12 of an hour, we want to find his unit rate, which is the amount of wall he can build per hour. To find Greg's unit rate, we divide the fraction of the wall built by the fraction of the hour spent building it. This calculation gives us:

Unit rate = (1/7) ÷ (1/12) = (1×12)/(7×1) = 12/7 = [tex]1\frac{5}{7}[/tex] walls per hour.

Therefore, the correct option is C: [tex]1\frac{5}{7}[/tex].

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{-3+1}{3}\implies -\cfrac{2}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{0}) \\\\\\ y+1=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x-1[/tex]

Answer:

its A 280

Step-by-step explanation:

Answer:

(-2 i) * (-3 i) = -6

Step-by-step explanation:

This is a product between imaginary numbers, so have in mind how the imaginary unit multiplies by itself: [tex]i\,*\,i = i^2=-1[/tex]

So let's work on the product:

[tex]-2\,i\,*\,(-3\,i)= (-2)\,*\,(-3)\,*\,i\,*\,i =(6)\,* i^2\,=(6)\,*\,(-1)= -6[/tex]

Answer:

Gianna makes $18 per hour.

Step-by-step explanation:

Given Gianna makes 90$ for 5 hours. That means she should make [tex]$ \frac{90}{5} $[/tex] $  = 18$ every hour.

Therefore we have:

a.

HOURS                    DOLLARS

  1                                   18

  2                                  36

  3                                  54

  4                                   72

  5                                   90

  6                                   108

  7                                   126

b.

For the tabular column mark Hours on the x - axis and Dollars on the Y - axis. It can be plotted from the above table easily.

c.

If Gianna works for 8 hours she would have made 8 X 18 = 144$.

So, she will earn 144$ in 8 hours.

d.

To make 60$ she would have to work [tex]$ \frac{60}{18} $[/tex] hours = 3.33 hours.

Answer:

Its 7 1/9! I hope this helped! Also what I used was mixed numbers calculator by calculator soup!  

Step-by-step explanation:

They are left with 0.51 pounds of clay.

Step-by-step explanation:

Given,

Amount of clay bought = 3.8 pounds

Amount used by Martha = [tex]\frac{1}{4}\ of\ clay[/tex]

Amount used by Martha = [tex]\frac{1}{4}*3.8=0.95\ pounds[/tex]

Amount left after Martha's use= Total amount - amount used by Martha

Amount left = 3.8 - 0.95 = 2.85 pounds

Amount used by Scott = [tex]\frac{2}{5}\ of\ amount\ left[/tex]

Amount used by Scott = [tex]\frac{2}{5}*2.85=\frac{5.70}{5}[/tex]

Amount used by Scott = 1.14 pounds

Amount left after Scott's use = Amount left after Martha's - Amount used by Scott

Amount left after Scott's use = 2.85 - 1.14 = 1.71 pounds

Amount used by Alison = 1.2 pounds

Amount left = Amount left after Scott's use - Amount used by Alison

Amount left = 1.71 - 1.2 = 0.51 pounds

They are left with 0.51 pounds of clay.

Keywords: subtraction, fraction

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Answer:

4x^2+20x+24

Step-by-step explanation:

(4x+8)(x+3)=4x^2+8x+12x+24=4x^2+20x+24

The value of f(x) * g(x) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3

We have two functions -

f(x) = 4x + 8

g(x) = x + 3

We have to determine f(x)*g(x).

A function in mathematics is an expression with a independent variable (x) in it. The variable is called independent because it is not dependent on any value to get its value. Function also has a dependent variable (y) whose value depend on x. Ex -

y = f(x) = ax + d

According to the question, we have -

f(x) = 4x + 8

g(x) = x + 3

Therefore -

f(x) * g(x) = (4x + 8)(x + 3) = 4x(x + 3) + 8(x + 3) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3

Hence, the value of f(x) * g(x) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3

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1x= y

Step-by-step explanation:

x being the weight and y being the cost

Final answer:

The equation representing the sentence is 'R *4 = 72', where R is Rita's height. Dividing both sides by 4 yields Rita's height as R = 18 units.

Explanation:

The sentence' 72 is the product of Rita’s height and 4' can be translated into the equation R *4 = 72, where R represents Rita's height in the appropriate unit (e.g., meters or feet).

To find Rita's height, you would divide both sides of the equation by 4, simplifying to R = 72 / 4. Therefore, Rita's height would be 18 units. In the context of the given examples, the algebraic representation involves setting up equations and solving for an unknown variable through techniques like cross multiplication and proportion.

Answer:

Probability that a student chosen randomly from the class plays basketball or baseball is  [tex]\frac{23}{30}[/tex] or 0.76

Step-by-step explanation:

Given:

Total number of students in the class = 30

Number of students who plays basket ball = 19

Number of students who plays base ball = 12

Number of students who plays base both the games = 8

To find:

Probability that a student chosen randomly from the class plays basketball or baseball=?

Solution:

[tex]P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]---------------(1)

where

P(A) = Probability of choosing  a student playing basket ball

P(B) =  Probability of choosing  a student playing base ball

P(A \cap B) =  Probability of choosing  a student playing both the games

Finding  P(A)

P(A) = [tex]\frac{\text { Number of students playing basket ball }}{\text{Total number of students}}[/tex]

P(A) = [tex]\frac{19}{30}[/tex]--------------------------(2)

Finding  P(B)

P(B) = [tex]\frac{\text { Number of students playing baseball }}{\text{Total number of students}}[/tex]

P(B) = [tex]\frac{12}{30}[/tex]---------------------------(3)

Finding [tex]P(A \cap B)[/tex]

P(A) = [tex]\frac{\text { Number of students playing both games }}{\text{Total number of students}}[/tex]

P(A) = [tex]\frac{8}{30}[/tex]-----------------------------(4)

Now substituting (2), (3) , (4) in (1), we get

[tex]P(A \cup B)= \frac{19}{30} + \frac{12}{30} -\frac{8}{30} [/tex]

[tex]P(A \cup B)= \frac{31}{30} -\frac{8}{30} [/tex]

[tex]P(A \cup B)= \frac{23}{30}[/tex]

Answer:

Step-by-step explanation:

 13x+2y=1

+ 5x-2y=-19

-------------------

18x=18

x=1

5x1-2y=-19

5-2y=-19

-2y=-19-5

-2y=14

-y=7

y=-7

x=1

y=-7

To solve the system, eliminate variables, find [tex]\( x = -1 \)[/tex], then substitute into an equation to get [tex]\( y = 7 \)[/tex].

To solve the system of equations [tex]\(13x + 2y = 1\)[/tex] and [tex]\(5x - 2y = -19\)[/tex], you can use the method of elimination.

First, let's eliminate one of the variables. We can eliminate [tex]\(y\)[/tex] by adding the two equations together:

[tex]\[ (13x + 2y) + (5x - 2y) = 1 + (-19) \][/tex]

This simplifies to:

[tex]\[ 13x + 5x = -18 \][/tex]

[tex]\[ 18x = -18 \][/tex]

Now, divide both sides by 18:

[tex]\[ x = \frac{-18}{18} \][/tex]

[tex]\[ x = -1 \][/tex]

Now that we have found [tex]\(x\)[/tex], we can substitute it into one of the original equations to find [tex]\(y\)[/tex]. Let's use the first equation:

[tex]\[ 13(-1) + 2y = 1 \][/tex]

[tex]\[ -13 + 2y = 1 \][/tex]

Add 13 to both sides:

[tex]\[ 2y = 1 + 13 \][/tex]

[tex]\[ 2y = 14 \][/tex]

Divide both sides by 2:

[tex]\[ y = \frac{14}{2} \][/tex]

[tex]\[ y = 7 \][/tex]

So, the solution to the system of equations is [tex]\(x = -1\)[/tex] and [tex]\(y = 7\)[/tex].

Answer:

[tex]10.50p+15\leq 65[/tex]

[tex]p\leq \frac{100}{21}[/tex]

Step-by-step explanation:

Let p represent pounds of Pumpkin Spice coffee.

We have been given that Lydia is at a coffee shop and knows  she can spend no more than $65  before tax. She sees this price list in  the coffee shop.

Item                                               Price per pound

Dark Roast Coffee                                 $7.50

Pumpkin Spice Coffee                         $10.50

Breakfast Tea                                       $23.50

Lydia wants to buy  2 pounds of  Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be [tex]\$7.50\times 2=\$15[/tex].

We are told that cost of each pound of Pumpkin Spice coffee is $10.50, so cost of 'p' pounds of Pumpkin Spice coffee would be [tex]10.50p[/tex].

Since Lydia can spend no more than $65  before tax, so the cost of 2 pounds of  Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.

We can represent this information in an inequality as:

[tex]10.50p+15\leq 65[/tex]

Therefore, our required inequality would be [tex]10.50p+15\leq 65[/tex].

[tex]10.50p+15-15\leq 65-15[/tex]

[tex]10.50p\leq 50[/tex]

Divide both sides by 10.50:

[tex]\frac{10.50p}{10.50}\leq \frac{50}{10.50}[/tex]

[tex]p\leq \frac{50*2}{10.50*2}[/tex]

[tex]p\leq \frac{100}{21}[/tex]

[tex]p\leq 4.76190[/tex]

Therefore, Lydia can buy less than or equal to [tex]\frac{100}{21}[/tex] pounds of Pumpkin Spice coffee.

Answer:

4 pounds of pumpkin spice coffee

Answer:

x=4

Step-by-step explanation:

Missing picture is attached.

As we can see in the picture drawn, there are two cord insecting outside the circle.

∴ we will use Intersecting secant theorem.

When two secant lines intersect each other outside a circle then the product of the length of the chord and the length of the part outside the circle are equal.  

Now, using the value in theoram as given in the picture.

⇒[tex]x\times 6= 3\times 8[/tex]

Dividing both side by 6

⇒ [tex]x= \frac{3\times 8}{6}[/tex]

∴x= 4

The value of function on x=1 is 0.5

Step-by-step explanation:

In order to find the value of a function on given input, the input is put at the place of variable in the function.

Given function is:

[tex]f(x) = (\frac{1}{2})^x[/tex]

We have to find the value of function on x = 1

Putting x = 1 in function

[tex]f(1) = (\frac{1}{2})^1\\= \frac{1}{2}\\= 0.5[/tex]

Hence,

The value of function on x=1 is 0.5

Keywords: Functions variables

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Answer:

$176.40

Step-by-step explanation:

Lets assume the order of events to be:

20 dollars discount first,

2% coupon discount, next

So, original cost is 200

Discount of 20 dollars, means that it now costs:

200 - 20 = $180

Now, we have a 2% discount coupon on it. We have to find 2% of 180 and subtract that from 180.

Note: 2% is 2/100 = 0.02

So,

180 * 0.02 = 3.6

So, final price would be:  180 - 3.6 = $176.40

Mark paid $176.40 for the shoes

The fraction 9/5 can be expressed as the sum of 1 (whole number) and 4/5 (fraction).

The fraction 9/5 can be expressed as a sum of a whole number and a fraction. First, divide 9 by 5 which will result in 1 with a remainder of 4. The 1 forms the whole number, and 4/5 forms the fraction. So, 9/5 is equivalent to 1 4/5, which means 1 (whole number) plus 4/5 (fraction) is equal to 9/5.

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Answer:

The value of x is 2[tex]\sqrt{29}[/tex] .

Step-by-step explanation:

Given as :

The area of Trapezoid = x² unit²

The measure of base 1 = [tex]b_1[/tex] = - 19 unit

The measure of base 2 = [tex]b_2[/tex] = 10 unit

The height of the mid segment = 8 unit

Now, From the Area of Trapezoid

i.e Area = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height

Or, x² = [tex]\dfrac{1}{2}[/tex] × (19 + 10) × 8

Or,  x² = [tex]\dfrac{8}{2}[/tex] × (29)

Or, x² = 4 × (29)

Or,  x² = 116

∴ x = [tex]\sqrt{116}[/tex]

I.e x = 2[tex]\sqrt{29}[/tex]

Hence, The value of x is 2[tex]\sqrt{29}[/tex] . Answer

Final answer:

Using the properties of a trapezoid's midsegment being the average length of the bases, the equation (10 + (x² - 19))/2 = 8 was solved to find that x equals 5.

Explanation:

The question revolves around the properties of a trapezoid and its midsegment. In a trapezoid, the midsegment (also called the median) is the segment that joins the midpoints of the non-parallel sides and is parallel to both bases.

The length of the midsegment is the average of the length of the two bases, which can be expressed as (base1 + base2) / 2.

Given that the midsegment is 8 units long, and one base is given as 10 units, let the other base be expressed as x² − 19 units. The formula for the midsegment becomes:

(10 + (x² − 19))/2 = 8

Now we solve for x:

10 + x² − 19 = 16

x² − 9 = 16

x² = 25

x = ± 5

Since the measure of a base cannot be negative, the positive root is the realistic solution:

x = 5

Answer:

No.

Step-by-step explanation:

Answer:

y=9

Step-by-step explanation:

substitution x=2 in equation

y= 3^2

y=9

Final answer:

To evaluate y=3^x for x=2, substitute x=2 into the expression y=3^x to find that y=9.

Explanation:

The given expression is y = 3^x. To evaluate y for x = 2, substitute x = 2 into the expression:

y = 3^2

y = 9

Therefore, y = 9 when x = 2.

Answer:

The answers are 10/24 and 9/24.

Step-by-step explanation:

Given:

Tim has 5/12 of a jar of blackberry jam and 3/8  of a jar of strawberry jam.

Now, to write using a common denominator.​

So, we get the multiples of denominator of the fractions to get common denominator:

12 - 12, 24, 36.

8  -  8, 16, 24.

Here we see that 24 is the common denominator.

Now, we multiply the numerator and denominator with the same number to get the common denominator of the fractions:

⇒  [tex]\frac{5}{12}=\frac{5\times 2}{12\times 2} =\frac{10}{24}[/tex]

⇒  [tex]\frac{3}{8}=\frac{3\times 3}{8\times 3} =\frac{9}{24}[/tex]

Therefore, the answers are 10/24 and 9/24.

Answer:

Step-by-step explanation:

Sec B

1) 5p⁻³ = 8*5⁻²      

p⁻³  = 2³*5⁻²/5            

p⁻³ =2³*5⁻³             { 1/a^m = a^-m}

p⁻³ = 5⁻³ /2⁻³            {a^m = 1/a^-m}

p⁻³ = (5/2)⁻³

p= 5/2

2) 4x²  = 81

x²  = 81/4

x²  = 9² /2²

x²  =(9/2)²

x = 9/2

3) 9^x/3 =81

9^x/3 = 9^2

Comparing the powers, x/3 = 2

                                         x = 2*3 =6

  x = 6

Answer: 37 1/3

Step-by-step explanation:

14/1÷3/8=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

14/1 × 8/3=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

14×8/1×3 = 112/3

This fraction cannot be reduced.

The fraction

112/3

is the same as

112÷3

Convert to a mixed number using

long division so

112/3=37 1/3

Therefore:

14/1 ÷ 3/8=37 1/3

Answer:

7/3

Step-by-step explanation:

7 1/3=22/3

22/3-5=22/3-15/3=7/3

Answer: 2 and 1/3

Step-by-step explanation: In this problem, we begin by subtracting the fractions. Since 5 has no fraction, imagine the fraction 0/3 so 1/3 - 0/3 is 1/3.

Next, subtract the whole numbers. 7 - 5 is 2 so 7 and 1/3 - 5 = 2 and 1/3.

Answer:

see explanation

Step-by-step explanation:

(A) Given

4(2x - 3) = 4 ( divide both sides by 4 )

2x - 3 = 1 ( add 3 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

(B)

As a check substitute x = 2 into the left side of the equation and if equal to the right side then it is the solution.

4(2(2) - 3) = 4(4 - 3) = 4(1) = 4 = right side

Hence x = 2 is the solution

Answer:

The solution of the given equation is x = 2.

Step-by-step explanation:

The given linear equation is,

[tex]4(2x-3)=4[/tex]

At first, we will eliminate '4' from the LHS by dividing both sides i.e., LHS and RHS by 4 because '4' is present in multiplication with the term containing unknown in LHS.

So, dividing both sides by '4', we get

[tex]\frac{4(2x-3)}{4} = \frac{4}{4}[/tex]

[tex]\implies 2x - 3 = 1[/tex]

Our next step will be to eliminate '3' from the LHS that is being subtracted from the term containg unknown variable. For this, we will add '3' on both sides of the above obtained equation.

So, adding '3' on both sides, we get

[tex]2x - 3 + 3 = 1 + 3[/tex]

[tex]\implies 2x = 4[/tex]

Now, we will eliminate '2' from the LHS that is in multiplication with the unknown variable 'x'.

For this, we will divide both sides of the above obtained equation by '2'.

So, dividing both sides by '2', we get

[tex]\frac{2x}{2}=\frac{4}{2}[/tex]

[tex]\implies x = 2[/tex]

CHECKING :

For this, we will substitute x = 2 in the LHS of the given equation and then check whether it is equal to RHS or not.

LHS = 4(2x - 3)

= 4(2 × 2 - 3)

= 4(4 - 3)

= 4 × 1

= 4

= RHS

So, the solution of the given equation is x = 2.

Answer:

7/2

Step-by-step explanation:

Answer:

[tex]\frac{3}{8}[/tex] yards of fabric.

Step-by-step explanation:

Jessica has [tex]\frac{9}{10}[/tex] yards of fabric and she cut [tex]\frac{5}{12}[/tex] of the length.

Therefore, Jessica has cut fabric of the length [tex]\frac{9}{10} \times \frac{5}{12} = \frac{3}{8}[/tex] yards.

This is the answer as a fraction in simplest form.

Now, Jessica used the expression to find the amount of fabric she cut as [tex] \frac{9}{10} \times \frac{5}{12}[/tex] was correct. ( Answer )

Answer:

i think its km.

Step-by-step explanation:

(please correct me if im wrong)