2/3 x 3/5 (multiply using Greatest Common Factor)

Answer:

There is only graph that starts with a line from y = h(x) = -4. Hence the required graph of the plot of h(x) is given by the second graph.

Therefore the correct option is the second graph.

Step-by-step explanation:

i) h(x) = [tex]\frac{x}{4}[/tex] - 4 for x ≤ 0. Therefore when x = 0 h(x) = -4

 There is only graph that starts with a line from y = h(x) = -4. Hence the required graph of the plot of h(x) is given by the second graph.

ii) For x < 0 we see from the from the equation in i) that h(x) will be more and more negative as the value of x decreases from 0.

iii) h(x) = [tex]\frac{x}{3}[/tex] - 3 for 0 < x ≤ 3 . Therefore when x = 0 , h(x) = -3 and again when x = 3  then x = -2 which is again the condition fulfilled by graph 2.

iv) h(x) = [tex]\frac{x}{2}[/tex] - 2 for x ≥ 4 . Therefore when x = 4 h(x) = 0 and as x increases from 4 we see that h(x) also increases to positive values.

This is also satisfied in the plot shown in the second graph.

v) Therefore the correct option is the second graph.

Answer:

Step-by-step explanation:

B

Answer:

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step

That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step.Because this is the correct way to do simplify the rational expression. And also because Nadine made a blender mistake in her operations in step

Step-by-step explanation:

Given that Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4

Their expression can be written as below

[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]

Nadine's first step is to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction

That is [tex]\frac{r^{20}s^{12}}{r^{-32}s^8}[/tex]

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4

That is [tex]r^{-13}s^{-1}[/tex]

Now simplify the given expression to check whose step is correct:

[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]

[tex]=(r^{-5}s^{-3}r^{-8}s^{2})^{-4}[/tex] ( using the property [tex]\frac{1}{a^m}=a^{-m}[/tex] )

[tex]=(r^{-5-8}s^{-3+2})^{-4}[/tex]

[tex]=(r^{-13}s^{-1})^{-4}[/tex]

Therefore [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex]

Therefore Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step.

That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step .Because this is the correct way to do simplify the rational expression.And also because Nadine made a blender mistake in her operations in step

Answer:

Step-by-step explanation:

f(x) = -4x^2 - 6x - 1  ........ g(x) = -x^2 - 5x + 3

find (f + g)(x)

-4x^2 - 6x - 1 + (-x^2 - 5x + 3) =

-4x^2 - 6x - 1 - x^2 - 5x + 3 =

-5x^2 - 11x + 2 <====

Answer: B

Step-by-step explanation:

Answer: 75

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

multiple of 15

7+5=12

Answer:

6

Step-by-step explanation:

0.75/0.125 = 6

6 x 0.125 would add up to be 0.75

To divide decimals, move the decimal point in both numbers to turn the divisor into a whole number. Multiply both numbers by the same power of 10 to get rid of the decimals. Then, divide the resulting whole numbers to get the answer.

To divide decimals, we can move the decimal point in both numbers to turn the divisor into a whole number. In this case, we can multiply both numbers by 1000 to get rid of the decimals. So, 0.75 becomes 750 and 0.125 becomes 125. Now, we can divide 750 by 125 to get the answer. Therefore, 0.75 divided by 0.125 is equal to 6.

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Answer:

Therefore,

The Length is longer than Width by 2 units.

[tex]Length=Width+2[/tex]

Step-by-step explanation:

Given:

Let the vertices of a Rectangle be  

A ( -7 , 6)

B ( 3 , 6)

C ( 3 , -6)

D ( -7 ,-6)

To Find:

Relation between Length and Width = ?

Solution:

First we will find the Length and Width of Rectangle by Distance Formula ,

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((3-(-7))^{2}+(6-6)^{2} )}[/tex]

[tex]l(AB) = \sqrt{((10)^{2}+(0)^{2} )}\\l(AB)=\sqrt{100}=10\ unit[/tex]

Similarly for BC we will have,

[tex]l(BC) = \sqrt{((3-3)^{2}+(-6-6)^{2} )}\\l(BC)=\sqrt{144}=12\ unit[/tex]

Now

Length = 12 units.

Width = 10 units.

Therefore,

Let Length be denoted by "L" and Width by "W" then

[tex]Length=Width+2=10+2=12\\\\\therefore L=W+2[/tex]

Therefore,

The Length is longer than Width by 2 units.

[tex]Length=Width+2[/tex]

Answer:

Answer is D

Step-by-step explanation:

10x+5y

10(6)+5(9)

60+45=

105

60 percent of 78 is the same as 65 percent of 72.

Step-by-step explanation:

Let,

x be the unknown number.

According to given statement;

60% of 78 = 65% of x

[tex]\frac{60}{100}*78=\frac{65}{100}x\\0.60*78=0.65*x\\46.8=0.65x\\0.65x=46.8\\[/tex]

Dividing both sides by 0.65

[tex]\frac{0.65x}{0.65}=\frac{46.8}{0.65}\\x=72[/tex]

Therefore;

60 percent of 78 is the same as 65 percent of 72.

Keywords: percentage, division

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Answer:

72

Step-by-step explanation:

sheesh kinda bussing

btw shesh

Answer:

Statement (reason):

∆ABC is an isosceles triangle with vertex angle B (Given).

Angle A is congruent to angle E (Given).

Angle BCA is congruent to angle DCE (Given).

BC is congruent to DC (Given).

∆ABC is congruent to ∆EDC (AAS).

AC is congruent to CE (CPCTC).

C is the midpoint of AE (Definition of midpoint).

Answer:

800

Step-by-step explanation:

1400 (the whole) / 7 (the whole) =200 (the partial) 200*4=800

Answer:

800

Step-by-step explanation:

4 out of 7 equals x out of 1400?

4/7 = x/1400

Cross multiply.

7x = 4 * 1400

Divide both sides by 7.

x = 4 * 1400/7

x = 4 * 200

x = 800

Answer: 800 dentists

Answer:

y = 3x +2

Step-by-step explanation:

The first answer

Answer:

[tex]m\angle RST=41^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The measure of the external angle is the semi-difference of the arcs it covers.

so

[tex]m\angle RST=\frac{1}{2}[arc\ RT-arc\ UV][/tex]

substitute the given values

[tex]m\angle RST=\frac{1}{2}[107^o-25^o][/tex]

[tex]m\angle RST=\frac{1}{2}[82^o][/tex]

[tex]m\angle RST=41^o[/tex]

The solution to the system of linear equations 4x - 2y = 8 and y = (3/2)x - 2 is x = 4 and y = 4, found by substituting y in the first equation with the expression from the second equation and solving for x.

The student is asking to solve a system of linear equations. The equations provided are:

4x - 2y = 8

y = (3/2)x - 2

We will solve this system using substitution since the second equation is already solved for y. Here are the steps:

Substitute y in the first equation with the expression from the second equation: 4x - 2((3/2)x - 2) = 8.

Simplify the equation: 4x - 3x + 4 = 8.

Solve the simplified equation for x: x + 4 = 8, which leads to x = 4.

Substitute x back into the second equation to find y: y = (3/2)4 - 2.

Calculate the value of y: y = 6 - 2, which leads to y = 4.

The solution to the system of equations is x = 4 and y = 4.

[tex]48 {in}^{2} [/tex]

Answer: B . 48 in²

Step-by-step explanation:

First o all complete the block and find the area

       The area of the completed block which looks like a rectangle

                                                                          =  L x B

                                                                          = 9 x 6

                                                                          = 54 in²

Step 2 : Find the area of the removed right angled triangle using the formula

                                                                         = ¹/₂b x h

where the base is 3 in and the height is 4 in

                                                                        = ¹/₂ x 3 x 4

                                                                        = 6 in².

Therefore, to find the area of the remaining  figure :

Area of the complete block less the area of the right  angled triangle

                                                                        = ( 54 - 6 ) in²

                                                                        = 48 in²

The option therefore is  B

Answer:

You multiply, the answer is 3,521.6084.

Step-by-step explanation:

Answer:

3521.6084

Step-by-step explanation:

Answer:

cos θ = -(√3)/2

tan θ = -1/√3

Step-by-step explanation:

[tex]\frac{\pi }{2} <\theta <\pi \ \ \ sin \ \theta = \frac{1}{2} \\[/tex]

Part A: find cos θ:

Using Pythagorean identity

sin²θ + cos²θ = 1

cos²θ = 1 - sin²θ = 1 - (1/2)² = 1 - 1/4 = 3/4

cos θ = ±√(3/4) = ±(√3)/2

∵(π/2) < θ < π  ⇒ ∴ cos θ = -(√3)/2

Part B: find tan θ:

sec θ = 1/(cos θ) = -2/√3

Using Pythagorean identity

tan²θ + 1 = sec²θ

tan²θ = sec²θ - 1 = 4/3 - 1 = 1/3

tan θ = ±√(1/3) = ± 1/√3

∵(π/2) < θ < π  ⇒ ∴ tan θ = -1/√3

[tex]1\frac{2}{3}[/tex] can be rewritten as 5/3 which is improper fraction.

A fraction represents a part of a whole.

Fractions are three types, Proper, improper and mixed fractions.

In proper fractions, denominator is less than numerator.

Improper fractions are fractions whose denominator is greater than numerator.

Mixed fractions can be converted to improper fractions.

The given fraction is improper fraction.

[tex]1\frac{2}{3}[/tex] is a mixed fraction.

((3×1)+2))/3=5/3

Hence, [tex]1\frac{2}{3}[/tex] can be rewritten as 5/3 which is improper fraction.

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Answer:

i dont know to be honest but i hope someone gives you the right answer that your looking for

Step-by-step explanation:

The missing number in the expression 5/8 + 2/? = 1 1/40 is 5. This was found by first converting the mixed number to an improper fraction and solving for the unknown denominator by finding a common denominator and simplifying the equation.

The question asks to find the missing number in the fraction equation 5/8 + 2/? = 1 1/40. To find the missing denominator, we can first convert the mixed number to an improper fraction, making the equation 5/8 + 2/? = 41/40. We then want the expression on the left to equal 41/40.

To begin, let's solve for the missing denominator by assuming it is 'x'. So, our equation is 5/8 + 2/x = 41/40. We need to get a common denominator to be able to add the fractions. The common denominator for 8, x, and 40 would be 40x. Now we multiply both sides by 40x to clear the fractions:

40x*(5/8) + 40x*(2/x) = 40x*(41/40)

Which simplifies to:

5*5x + 80 = 41x

Now, we move like terms to one side to solve for x:

80 = 41x - 25x

Which simplifies to:

80 = 16x

Dividing both sides by 16 gives us:

x = 5

Therefore, the missing number in the original equation is 5.

Answer:

5/26

Step-by-step explanation:

red / all = 10 / (15+5+10+12 +10)

=10 / 52

=5/26

Probability of choosing a red candy is 5 / 26

Given that:

Number of brown candy = 15

Number of blue candy = 10

Number of red candy = 10

Number of green candy = 5

Number of yellow candy = 12

Find:

Probability of choosing a red candy

Computation:

Total number of candies = 15+5+10+12+10

Total number of candies = 52

Probability of choosing a red candy = Number of red candy / Total number of candies

Probability of choosing a red candy = 10 / 52

Probability of choosing a red candy = 5 / 26

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Answer:

The possible distance in miles that Amelia can drive without exceeding her budget is 270 miles

Step-by-step explanation:

Given:

Amelia's budget for renting a car for a day trip = $ 89

Rental cost  = $35

cost per mile  = $0.20

To Find:

The possible distance in miles that Amelia can drive without exceeding her budget = ?

Solution:

Let M be the number of miles

The equation representing the situation can be

Total budget  less than or equal to rental + (number of mile x cost per mile)

That is

[tex]89 \leq 35 +(0.20 \times M)[/tex]

Solving for M, we get

[tex]89-35 \leq 0.20 M\\[/tex]

[tex]54 \leq 0.20M\\[/tex]

[tex]M \leq \frac{54}{0.20}[/tex]

[tex]M \leq 270[/tex]

Amelia's budget: $89. Rental: $35/day + $0.20/mile. Inequality: [tex]\( M \leq 270 \)[/tex] . Amelia can drive ≤270 miles.

let's break it down step by step.

1. Setting up the total cost equation:

  We're given that the rental cost is $35 per day plus $0.20 per mile. So, the total cost [tex]\( C \)[/tex] can be represented as:

 [tex]\[ C = 35 + 0.20M \][/tex]

  Where [tex]\( M \)[/tex] is the number of miles driven.

2. Setting up the inequality:

  We're told that Amelia can spend no more than $89. Therefore, we set up the inequality:

 [tex]\[ 35 + 0.20M \leq 89 \][/tex]

  This inequality represents that the total cost (rental cost plus mileage cost) should be less than or equal to $89.

3. Solving the inequality:

  To solve for [tex]\( M \),[/tex] we first subtract $35 from both sides to isolate the term involving [tex]\( M \):[/tex]

 [tex]\[ 0.20M \leq 89 - 35 \] \[ 0.20M \leq 54 \][/tex]

4. Dividing both sides by 0.20 to isolate [tex]\( M \):[/tex]

  [tex]\[ M \leq \frac{54}{0.20} \] \[ M \leq 270 \][/tex]

5. Interpreting the result:

  The inequality [tex]\( M \leq 270 \)[/tex] tells us that Amelia can drive at most 270 miles without exceeding her budget of $89.

So, in detail, Amelia can drive a maximum of 270 miles to stay within her budget. Any distance beyond that would exceed her budget of $89 for the day trip.

Answer:

5% less of 180, or 95% of 180

Step-by-step explanation:

FInd 10% of 180, 18, multiply 18 by 9.

18 x 9 = 162, find half of 18 which is 9.

Add to 162.

162 + 9 = 171.

Therefore,

5% less of 180 is 171.

The  absolute value of the melting point of neon greater than the absolute value of the melting point of hydrogen.

Step-by-step explanation:

In positive numbers, when the number gets larger then it is considered to be the greatest number.

for example: 20 > 5.

Meanwhile, For negative numbers, when the number gets larger then it is considered to be the smallest.

For example: -21 > - 40.

From the given table, we are given with the values of Melting point:

Hydrogen= -259.

Neon = -248.

Oxygen = -218.

We have to compare the melting points of hydrogen and neon,

⇒ - 248 > - 259.

Thus the melting point of the neon is greater than the melting point of the hydrogen.

James has pennies, nickles and dimes in his bank. he has more than $1.60 and less than $2.00 in the bank. there are 5 times as many pennies as dimes. there is an equal number of nickels and dimes. what is the exact amount of money in his bank?

Answer:

The exact amount of money in his bank is $ 1.8

Solution:

Let "p" be the number of pennies

Let "d" be the number of dimes

Let "n" be the number of nickels

Given that,

There are 5 times as many pennies as dimes

Number of pennies = 5 times the number of dimes

p = 5d ----------- eqn 1

There is an equal number of nickels and dimes

n = d -------- eqn 2

We know that,

value of 1 dime = 0.10 dollar

value of 1 nickel = 0.05 dollar

value of 1 penny = 0.01 dollar

The total value of coins is:

total value = d(0.10) + n(0.05) + p(0.01)

Substitute eqn 1 and eqn 2

total value = d(0.10) + d(0.05) + 5d(0.01)

total value = 0.2d

Given that he has more than $1.60 and less than $2.00 in the bank

Therefore, 0.2d must be greater than 1.60 and less than 2.00

Try for d = 8

total value = 0.2 x 8 = 1.6

But value must be greater than 1.6

Try for d = 9

total value = 0.2 x 9 = 1.8

Thus 1.8 is greater than 1.60 and less than 2.00

Therefore, the exact amount of money in his bank is $ 1.8

Answer:

6. a=22, b= 11

7. a =4, b=

[tex]2 \sqrt{2} [/tex]

Step-by-step explanation:

6.

[tex] \tan(30) = \frac{b}{11 \sqrt{3} } \\ or \: \: ( \frac{1}{ \sqrt{3} } ) = \frac{b}{11 \sqrt{3} } \\ or \: \: \: b = 11 \\ and \: \sin(30) = \frac{11}{a} \\ or \: \ \: \frac{1}{2} = \frac{11}{a} \\ \: \: \: \: a = 22[/tex]

Hope u understand....

Jason needs to ride 0.75 miles more to reach the end of the path

Solution:

Given that Jason begins at the start of a path and rides his bike [tex]11\frac{1}{2}[/tex] miles on the path

From given information,

[tex]\text{Total length of path } = 12\frac{1}{4} \text{ miles } = \frac{4 \times 12 + 1}{4} = \frac{49}{4} \text{ miles }[/tex]

[tex]\text{Distance covered already } = 11\frac{1}{2} \text{ miles } = \frac{11 \times 2 +1}{2} = \frac{23}{2} \text{ miles }[/tex]

To find: Distance in miles Jason must ride to reach the end of the path

Thus subtracting distance already covered from total distance, we get the distance Jason must ride to reach the end of the path

[tex]\text{Distance needed } = \text{Total length of path } - \text{Distance already covered }\\\\\text{Distance needed } = \frac{49}{4} - \frac{23}{2}\\\\\text{Distance needed } =\frac{49}{4} - \frac{23 \times 2}{2 \times 2}\\\\\text{Distance needed } =\frac{49}{4} - \frac{46}{4} = \frac{49-46}{4} = \frac{3}{4} = 0.75[/tex]

Thus Jason needs to ride 0.75 miles more to reach the end of the path

Answer:

The statement that is true about deep currents is :

They move cold water along the bottom of the ocean from the Atlantic Ocean to the Pacific Ocean.

The correct option for this is the second option, Option B.

Step-by-step explanation:

The statement that is true about deep currents is :

They move cold water along the bottom of the ocean from the Atlantic Ocean to the Pacific Ocean.

Answer: x² + y² + 22x + 16y + 169 = 0

Step-by-step explanation:

Equation of a circle with center (a,b) , and radius r i.e center is  not the origin

The equation becomes

( x - a )² + ( y - b )² = r² ------------------------------ 1

a = -11, b = -8

[( x - (-11 )]²  +  [( y - (-8)]² = 4²

      ( x + 11 )² + ( y + 8 )² = 4²

Carry out expansion

x² + 22x + 121 +  y² + 16y + 64 = 16

Rearrange the expression,

x² + y² + 22x + 16y + 121 + 64 - 16 = 0

x² + y² + 22x + 16y + 169 = 0

The equation of the circle is

x² + y² + 22x + 16y + 169 = 0