Dina's mother is four times older than Dina. Dina is 35 years younger than her father. Dina's father was 5 years older than Dina's mother when Dina was born. How old is Dina now?

Answer:

? = 4

Step-by-step explanation:

4/5 = 4/1 x 1/5

4/5 = 4/5

The equation of the line containing the points (3,1) (9,3) and (27,9) is y = 1 / 3x

The equation of a line can be found as follows:

y = mx + b

where

Therefore,

using  (3,1) (9,3)

m =  3 - 1 / 9 - 3 = 2 / 6 = 1 / 3

using (3, 1)

1 = 1 / 3(3) + b

1 = 1 + b

b = 0

Therefore,

y = 1 / 3x

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The angle between their paths to the nearest degree is 68⁰.

first displacement, a = 15 km/h  x (45/60)

first displacement, a = 11.25 km

second displacement, b = 18 km/h  x (45/60)

                                     b = 13.5 km

c² = a² + b² - 2ab(cosθ)

2ab(cosθ) = a² + b² - c²

cosθ =  (a² + b² - c²)/(2ab)

cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)

cosθ = 0.371

θ = arc cos(0.371)

θ = 68.22 ⁰

Thus, the angle between their paths to the nearest degree is 68⁰.

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The current drawn by 9 identical motors will be 124.2 amps current

Current is the flow of electrical charge carriers like electrons. Current flows from negative to positive points. The SI unit for measuring electric current is the ampere (A). One ampere of current is defined as one coulomb of electrical charge moving past a unique point in a second.

since , one motor of 2hp draws = 13.8 amps current

hence , 9 identical motor will pull = 13.8 * 9 (each will pull same amount of current )

                                                         = 124.2 amps current

The current drawn by 9 identical motors will be 124.2 amps current

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Fencer X attacks. Fencer Y makes a parry, and scores a riposte to the valid target of Fencer X. During the parry, Fencer Y strikes Fencer Xs mask with the bell guard. annual the touch fencer Y recieves  a RED CARD.

what are the fencing rules ?

Penalty cards or flags are also used in modern fencing. Each card has a unique meaning. A fencer who receives a yellow card is warned, but no further action is taken. A fencer who receives a red card is warned, and their opponent receives a touch. A fencer who receives a black card is disqualified from the competition and may be disqualified from the tournament, expelled from the venue, or suspended from future tournaments if the offence is serious. However, black cards are rarely given to fencers. It should be noted that spectators can (and occasionally are) carded or expelled.

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Option D. What we can conclude is that  If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

An operation is done on a first column of numbers. When this operation is repeated on the second column, we would have option D.

If the sum of the numbers that are in the third can be seen to be greater than three, then the sums are not going to be seen as equal

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One column of numbers consists of 28, 42, and 14. When the digits of the numbers are added together, the result is 2 + 8 + 4 + 2 + 1 + 4 = 21, and when the digits of 21 are then added together, the end result is 2 + 1 = 3. If the same process is performed on the numbers in a second column, what can be concluded?

A. If the end result from the second column is also 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

B. If the end result from the second column is not 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

C. If the end result from the second column is also 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

D. If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

Answer:

4x^04x^04x^04x^1 which equals 256

Step-by-step explanation:

The 4 outside of the parentheses says take what you have outside of the parentheses and multiply it by itself that may times.

x raised to the zero is 1, so you are just left with 4x4x4x4 or 256

Answer:

[tex] y = \pm \sqrt{\dfrac{x - 7}{6}} [/tex]

Step-by-step explanation:

f(x) = 6x² - 7

y = 6x² - 7

x = 6y² - 7

6y² = x - 7

[tex] y^2 = \dfrac{x - 7}{6} [/tex]

[tex] y = \pm \sqrt{\dfrac{x - 7}{6}} [/tex]

Answer: A

Step-by-step explanation:

[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]

The expression which is equivalent to [tex]5 log_{10}x+log_{10}20-log_{10}10[/tex] is

[tex]$5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(20x^5)-1[/tex].

A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable.

Product Rule Law: [tex]log_{a} (MN) = log_{a} M + log_{a} N[/tex]

Quotient Rule Law: [tex]log_{a} (M/N) = log_{a} M - log_{a} N[/tex]

Power Rule Law: [tex]log_{a}M^{n} = n log_{a} M[/tex]

Given: [tex]5 log_{10}x+log_{10}20-log_{10}10[/tex]

[tex]5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(x^5) +log_{10}20 -log_{10}10[/tex]

apply the law of logarithm

[tex]5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(x^5*20/10)[/tex]

[tex]5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(x^5*2)[/tex]

[tex]5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(2x^5)[/tex]

Another possible equivalent expression is:

[tex]$5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(x^5*20)-log_{10}10[/tex]

[tex]$5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(20x^5)-log_{10}10[/tex]

Substitute the value of [tex]log_{10}10 = 1[/tex]

[tex]$5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(20x^5)-1[/tex]

Therefore, the correct answer

[tex]$5 log_{10}x+log_{10}20-log_{10}10 = log_{10}(20x^5)-1[/tex].

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Answer:

screenshot attached of graph

Step-by-step explanation:

Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

Step-by-step explanation:

Since there is 2 unknown variable ,

so we need 2 equation to find their values.

The value of w from the given equation is w=(x-3y+1)/3.

Given  an equation x=3(y+w)-1 and we have to find the value of w in terms of x and y.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation.

The given expression is x=3(y+w)-1 and we have to find the value of w. To find the value we have to first solve the right side of the equation.

x=3y+3w-1

Now take w at one end and all other variables in other end.

3w=x-3y+1

Now divide both sides by 3.

3w/3=(x-3y+1)/3

Now cancel 3 from numerator and denominator in left side.

w=(x-3y+1)/3

Hence the value of w in the equation x=3(y+w)-1 is w=(x-3y+1)/3.

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For two bathroom remodel estimate budget is $[tex]20000[/tex] for both remodels. when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $[tex]100[/tex] less than the budgeted .So the actual cost of two bathroom remodel is $ [tex]19800[/tex] and the different of actual and expected budgets is $[tex]200[/tex]

How can we find the actual costing of the bathroom remodel ?

Expected estimate budget of two bathroom's remodel is $[tex]20000[/tex]

So budget of one bathroom remodel is

[tex]20000/2\\=10000[/tex]

All supplies are come except for two vanities which were each $[tex]100[/tex]

So for two bathroom remodels

[tex]=2*100\\=200[/tex]

So the actual cost of remodel of both bathroom is

[tex]=20000-200\\=19800[/tex]

And difference between actual and estimated cost is

[tex]=20000-19800\\=200[/tex]

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Answer:

5x - y = 9

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = 5x - 9 ( subtract 5x from both sides )

- 5x + y = - 9 ( multiply through by - 1 )

5x - y = 9 ← in standard form

Answer:

The answer is the first option; 6^1/12

Step-by-step explanation:

We can simplify the question by using the radical rule to rewrite it as
6^1/3 ÷ 6^1/4

Then we use exponent rule which states that when we are dividing exponents of the same base, we have to subtract them. We see that the exponents are 1/3 and 1/4. So we use basic fractional division, here's the subtraction:

= 1/3 - 1/4
= 4/3 - 3/4 (we criss-crossed)
= 1/12 (we subtracted the denominators and multiplied the denominators)

Now that we have subtracted the exponents, we can write the answer as 6^1/12

Answer:

Option #1: [tex]6\frac{1}{2}[/tex]

Step-by-step explanation:

#1: Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] and [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]:

[tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}} * \frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]

#2: Combine and simplify the denominator:

- Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] by [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] = [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6} \sqrt[4]{6}^3}[/tex]

- Raise [tex]\sqrt[4]{6}[/tex] to the power of 1

- Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6}^{1+3}}[/tex]

- Add 1 and 3

- Rewrite [tex]\sqrt[4]{6}^4[/tex] as 6: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^3}{6}[/tex]

#3: Simplify the numerator:

- Rewrite the expression using the least common index of 12: [tex]\frac{\sqrt[12]{6^4} \sqrt[12]{216^3}}{6}[/tex]

- Combine using the product rule for radicals: [tex]\frac{\sqrt[3]{6^4 *216^3}}{6}[/tex]

- Rewrite 216 as [tex]6^3[/tex]: [tex]\frac{\sqrt[3]{6^{4}*(6^{3})^{3}}}{6}[/tex]

- Multiply the exponents in [tex](6^{3})^3[/tex]: [tex]\frac{\sqrt[12]{6^{4}*6^{9}}}{6}[/tex]

- Use the power rule [tex]a^{m}a^{n}=a^{m+n}[/tex] to combine exponents and add [tex]4+9[/tex]:

[tex]\frac{\sqrt[12]{6^{13}}}{6}[/tex]

- Raise 6 to the power of 16: [tex]\frac{\sqrt[12]{13060694016}}{6}[/tex]

- Rewrite 13060694016 as [tex]6^{12}*6[/tex]: [tex]\frac{\sqrt[12]{6^{12}*6}}{6}[/tex]

- Pull terms out from under the radical: [tex]\frac{6\sqrt[12]{6}}{6}[/tex]

#4: Cancel the common factor of 6:

[tex]\frac{\sqrt[12]{6}}{6}=6\frac{1}{2}[/tex]

The correct simplified answer for [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] is Option #1: [tex]6\frac{1}{2}[/tex].

in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

Standard form is simply a value with an exponential powerl

Given the values;

It is important to note that any number to the power of O is equivalent to 1

So, we have

10^ 0 = 1

4( 10^-3) = 37

5(10^3) = 5000

Now, let's substitute the values

(10°) + 4 (10-3) + 5 (10³)

It is equivalent to

⇒1 + 4 × 10^-3 + 5 × 10^3

⇒1 + 37 + 5000

Add the values

= 5038

Let's convert it to standard form, we have

= 5. 04 × 10 ^3

Thus, in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

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Answer:

118

Step-by-step explanation:

The total area is the area of the large rectangle in the middle plus the areas of the two triangles.

The length of the entire rectangle is 5 cm + 5 cm + 4 cm = 14 cm.

The width of the rectangle is 7 cm.

Each triangle has a base of 4 cm and a height of 5 cm.

A = LW + 2 × (1/2)bh

A = (14 cm)(7 cm) + (4 cm)(5 cm)

A = 98 cm² + 20 cm²

A = 118 cm²

The Time taken by Jacob to run the dash race is (80 - t) seconds

We are told that;

Total distance for the dash race = 500 yards

Time taken by Jacob to run the dash race = 80 seconds

Now, we are told that Juan ran the same dash race but used t less seconds than Jacob. Thus;

Time taken by Jacob to run the dash race = (80 - t) seconds

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The solution to the given inequality is y < 5

Inequality are equations  not separated by an equal sign. Given the following parameters

15 > y + 10

Subtract 10 from both sides

15 - 10 > y + 10 - 10

5 > y

Swap

y < 5

Hence the solution to the given inequality is y < 5

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The final temperature at the time Tariq goes to bed was +12 degrees, represented as integers.

The initial temperature of the day was 0 degrees.

The temperature rose 23 degrees in the afternoon.

This implies that we move +23 on the scale, represented as an integer.

The temperature decreased 11 degrees in the evening.

This implies that we move -11 on the scale, represented as an integer.

This moves the temperature to +23 -11 = +12 degrees, represented as an integer.

Thus, the final temperature at the time Tariq goes to bed was +12 degrees, represented as integers.

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Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V

-3|0+2|+4=-2

-3|1 +2|+4= -5

-3|2+2|+4= -8

-3|-1+2|+4=1

+3|-2+2|+4=1

Step-by-step explanation:

Answer:

A varicocele measures more than 2 mm in diameter.

Step-by-step explanation:

pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.

The logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

The equation is given as

13^2=169

Take the logarithm of both sides

log(13^2) = log(169)

This gives

2log(13) = log(169)

Divide both sides by log(13)

[tex]\log_{13}(169) = 2[/tex]

Hence, the logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

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The relative frequency of students who have three siblings is 25% given that there are 60 students in a class in which 5 have no siblings, 26 have one sibling, 14 have two siblings and 15 have three siblings. This can be obtained by using the formula for relative frequency.

Given that,

total number of students in the class = 60

number of students who have no sibling = 5

number of students who have 1 sibling = 26

number of students who have 2 sibling = 14

number of students who have 3 sibling = 15

Formula for relative frequency = f/n, where f is the number of times the data occurred, n is the total number of frequencies.

Therefore,

relative frequency of students who have three siblings = 15/60 = 0.25

In percentage ⇒ 0.25 × 100 = 25%

Hence the relative frequency of students who have three siblings is 25% given that there are 60 students in a class in which 5 have no siblings, 26 have one sibling, 14 have two siblings and 15 have three siblings.

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The surface area of prism 1 is 36 cm²

From the question, we are to calculate the surface area of prism 1

From the given information, we have that the two hexagon-based prism are similar

Since the shapes are similar, we can write that

(Length of a side in prism 1)² / (Length of the similar side in prism 2)² =

Area of prism 1 / Area of prism 2

From the given information,

Length of a side in prism 1 = 3 cm

Length of the similar side in prism 2 = 8 cm

Area of prism 2 = 256 cm²

Thus,

3² / 8² = Area of prism 1  / 256

Area of prism 1 = (256 × 3²)/ 8²

Area of prism 1 = (256 × 9)/ 64

Area of prism 1 = (2304)/ 64

Area of prism 1 = 36 cm²

Hence, the surface area of prism 1 is 36 cm²

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The quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively

From the given equation, we have to find

= 3/4 ÷ 1/8

First , we take the denominator of the second fraction to be the numerator, we have

=

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

Multiply through

=

[tex] \frac{24}{4} [/tex]

=

[tex]6[/tex]

To find the quotient of 3 by 1/6

=

[tex]3 \times \frac{1}{6} [/tex]

=

[tex] \frac{3}{6} [/tex]

=

[tex] \frac{1}{2} [/tex]

Thus, the quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively

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