systems of equations
15x-4y=62
5x+8y=86

Answer:

0,1 is greater because...

Answer:0,1

Step-by-step explanation:

The height of the branch is 9.54 ft

Step-by-step explanation:

Apply Pythagorean relationship in this question where the length of the ladder is the hypotenuse, and the distance from the tree base is the shortest side.Finding the height will be;

a²+b²=c²

a²+3²=10²

a²=10²-3²

a²=100-9

a²=91

a=√91=9.54 ft

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Answer:

Step-by-step explanation:

Problems like these are aided immensely by your knowledge of multiplication tables.

1) 36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6

  27 = 1·27 = 3·9

The greatest common factor is 9, so the sum can be written as 9(4+3).

__

2) 45 = 1·45 = 3·15 = 5·9

  25 = 1·25 = 5·5

The greatest common factor is 5, so the sum can be written as 5(9+5).

__

3) 16 = 1·16 = 2·8 = 4·4

  72 = 1·72 = 2·36 = 3·24 = 4·18 = 6·12 = 8·9

The greatest common factor is 8, so the sum can be written as 8(2+9).

Answer:

[tex]z=12[/tex]

Step-by-step explanation:

The lines a and b intersect at point D. Angles with measures [tex](5z+8)^{\circ}[/tex] and [tex](4z+20)^{\circ}[/tex] are vertical angles.

Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.

Congruent angles have equal measures.

Hence,

[tex]5z+8=4z+20\\ \\5z-4z=20-8\\ \\z=12[/tex]

Answer:

12

Step-by-step explanation:

Answer:

B. SSS

Step-by-step explanation:

All of the sides are the same

SSS postulate proves that the two triangles are congruent.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

From the figure we have two triangles named as FED and CBA

Now, In triangles FED and CBA

FE = AC

ED = BA

FD = BC

So, by SSS Congruency Criteria triangles FED and CBA are Congruent.

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Answer:

-4

Step-by-step explanation:

6 times 4 equals 24

24 minus 12 equals 12

12 divided by 3 equals 4

4 minus 8 equals -4

(btw i did this in the order from the question and not BIDMAS )

Answer: 8/5 or 1 ⅗ acres

Step-by-step explanation:

Answer:

So she need [tex]\frac{5}{36}\ cups[/tex] more to put in.

Step-by-step explanation:

Given:

Recipe for cookies calls for 3 1/4 cups of sugar.

Amy has already put three and one nine cups.

Now, to find the number of cups she need to put in.

Number of cups of sugar for recipe calls = [tex]3\frac{1}{4} =\frac{13}{4}\ cups.[/tex]

Amy has already put = [tex]3\frac{1}{9} =\frac{28}{9}\ cups.[/tex]

So, to get the number of cups she need to put in we subtract number of cups of sugar for recipe calls from number of cups of sugar for recipe calls:

[tex]\frac{13}{4} -\frac{28}{9}[/tex]

Subtracting by taking the same denominator:

[tex]=\frac{117-112}{36}[/tex]

[tex]=\frac{5}{36}[/tex]

Therefore, so she need [tex]\frac{5}{36}\ cups[/tex] more to put in.

Answer:

24

Step-by-step explanation:

First find the exterior angle: 180 - 165 = 15

Then 360 ÷ 15 because 360 divided by he exterior angle of a regular polygon is equal to the number of sides.

Answer:

Hello, 24

Step-by-step explanation:

Ingerior angle = 165

Exterior angle = 180 - 165 = 15

The sum of exterior angles of any polygon is 360

Number of sides = 360/15 = 24 A polygon is any two dimensional shape formed with the straight lines. Triangles, pentagons, quadrilaterals, and hexagons are all examples of the polygons. The name itself tells as to how many sides the shape has. For example, a triangle has three sides, whereas a quadrilateral has four sides.

Thus, when the regular polygon have if each of its interior angle is 165° then,

The corresponding exterior angle must be 180-165 = 15°

The sum of ALL the exterior angles is 360°

Sides of exterior angles is 360/15 = 24

Therefore the number of sides a regular polygon will have is 24                           Have a Awesome Day!

The graph representing the solution to the system of inequalities y < 2x - 5 and y > -3x + 1 would have a dashed line for the first inequality and a solid line for the second one, with the intersected shading to the left of the lines.

The student's question centers around identifying which graph depicts the solution to the given system of linear inequalities: y < 2x - 5 and y > -3x + 1. The solution to a system of inequalities is represented by the area of intersection between the two shaded regions of the graphs. The first inequality, y < 2x - 5, is a line with a positive slope that passes through (0, -5) and the shading is below the line because 'y' is less than the expression on the right. The second inequality, y > -3x + 1, is a line with a negative slope that passes through (0, 1), and the shading is above the line because 'y' is greater than the expression on the right. Based on these conditions, the correct graph would be the one with a dashed line (indicating 'less than' or 'greater than' but not 'equal to') for the first equation and a solid line (indicating 'less than or equal to' or 'greater than or equal to') for the second equation where the shading on the left side of the lines intersect.

Remember, the slope of a line indicates how steep the line is and is calculated by rise over run. The y-intercept of a line is where the line crosses the y-axis. These key features, along with the type of inequality symbol, determine where and how to shade the graph for a system of linear inequalities.

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Answer:

2.339×10^3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

2.339×10^3

The factors of given expression are: -5 and 3/4

Step-by-step explanation:

Given equation is:

[tex]4x^2+17x-15[/tex]

Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15

[tex]4x^2+20x-3x-15[/tex]

[tex]= 4x(x+5) - 3(x+5)[/tex]

[tex]=(4x-3)(x+5)[/tex]

Now

[tex]4x-3 = 0\\4x = 3\\x = \frac{3}{4}[/tex]

[tex]x+5 = 0\\x = -5[/tex]

Hence,

The factors of given expression are: -5 and 3/4

Keywords: Quadratic equation, factors

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A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults? . How many who paid were seniors?

Answer:

There were 69 adults and 284 seniors

Solution:

Let "a" be the number of adults

Let "s" be the number of seniors

Cost of 1 adult = $ 8

Cost of 1 senior = $ 4

On a particular day when 353 people paid an admission

Therefore,

number of adults + number of seniors = 353

a + s = 353

a = 353 - s ---------- eqn 1

The total receipts were 1688 dollars

Therefore, we frame a equation as:

number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688

[tex]a \times 8 + s \times 4 = 1688[/tex]

8a + 4s = 1688 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

8(353 - s) + 4s = 1688

2824 -8s + 4s = 1688

4s = 2824 - 1688

4s = 1136

Substitute s = 284 in eqn 1

a = 353 - 284

Thus there were 69 adults and 284 seniors in movie theater

there were 55 adults and 284 seniors who paid admission.

Let's denote:

- ( A ) as the number of adults.

- ( S ) as the number of seniors.

Given:

- The price for adults is $9.

- The price for seniors is $5.

- The total number of people who paid admission is 339.

- The total receipts were $1915.

We can set up a system of equations based on the given information:

1. The total number of people who paid admission:

[tex]\[ A + S = 339 \][/tex]

2. The total receipts:

[tex]\[ 9A + 5S = 1915 \][/tex]

Now, we can solve this system of equations.

Let's solve equation 1 for one of the variables (let's solve for ( A )):

[tex]\[ A = 339 - S \][/tex]

Now, substitute this expression for( A ) into equation 2:

[tex]\[ 9(339 - S) + 5S = 1915 \][/tex]

Now, solve for \( S \):

[tex]\[ 3051 - 9S + 5S = 1915 \][/tex]

[tex]\[ -4S = 1915 - 3051 \][/tex]

[tex]\[ -4S = -1136 \][/tex]

[tex]\[ S = \frac{-1136}{-4} \][/tex]

[tex]\[ S = 284 \][/tex]

Now, we can find ( A ) using the value of ( S ) we found:

[tex]\[ A = 339 - 284 \][/tex]

[tex]\[ A = 55 \][/tex]

So, there were 55 adults and 284 seniors who paid admission.

complete question given below:

A movie theater charges 9$ for adults and 5 for seniors.on a particular day when 339 people paid an admission,the total receipts were 1915$ how many who paid were adults and how many who paid were seniors

the graphs picture is not provided (incomplete question. explanation:

Answer:bar graphs and pie charts

Step-by-step explanation:

edge 2021

Final answer:

Calculating the least common multiple (LCM) of 3 and 5 to determine that 6 students will receive both a medal and a ribbon at a swim meet of 100 students.

Explanation:

To find the number of students at the swim meet who will receive both a medal and a ribbon, we need to look for the common multiples of 3 and 5, as medals are given to every 3rd finisher and ribbons to every 5th finisher. The least common multiple (LCM) of 3 and 5 is 15, which means every 15th student will receive both a medal and a ribbon. Since there are 100 students, we simply divide 100 by 15 and then take the integer part of the result, because we can't have a fraction of a person.

100 ÷ 15 equals approximately 6.66. The integer part is 6, which means 6 students will receive both a medal and a ribbon.

Answer:

11.5

Step-by-step explanation:

(11+12)/2=11.5

Answer:

  480

Step-by-step explanation:

Let h represent the number of high-quality downloads. Then the total download size is ...

  4.1h +2.7(1130-h) = 3723

  1.4h = 672 . . . . . . . . . . . . . . subtract 2.7·1130 = 3051

  h = 480 . . . . . . . divide by 1.4

There were 480 downloads of the high-quality version.

Answer:

1/2

Step-by-step explanation:

The y-intercept is [tex]\frac{1}{2}[/tex].

Given that f(x) = 4x-2.

To find the inverse function:

1) Write f(x) = y

2) Switch x and y.

3) Solve for y.

4) Write [tex]y=f^{-1}\left(x\right)[/tex].

So,

[tex]f(x) = 4x - 2\\y=4x-2\\x=4y-2\\4y=x+2\\y=\frac{\left(x+2\right)}{4}\\y=\frac{1}{4}x+\frac{2}{4}\\y=\frac{1}{4}x+\frac{1}{2}\\f^{-1}\left(x\right)=\frac{1}{4}x+\frac{1}{2}[/tex]

Comparing this with y=mx+b,

b = y-intercept = [tex]\frac{1}{2}[/tex]

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Answer:

B. right

Step-by-step explanation:

In the bottom left corner there is a square. The square represents a 90 degree angle. A 90 degree angle is named a right angle.

Answer:

14838388÷+113

Step-by-step explanation:

because it has two zeros

Answer:

its b

Step-by-step explanation:trust

See the graph below

We need to remember the following rules:

[tex]For \ any \ function \ f(x) \ we have: \\ \\ \\ \bullet \ g(x)=f(x-k) \ Translation \ k \ units \ to \ the \ right \\ \\ \bullet \ g(x)=f(x+k) \ Translation \ k \ units \ to \ the \ left \\ \\ \bullet \ g(x)=f(x)+c \ Translation \ c \ units \ up \\ \\ \bullet \ g(x)=f(x)-c \ Translation \ c \ units \ down \\ \\ With \ c>0 \ and \ k>0[/tex]

Here we know that The function y = log (x) is translated 1 unit right and 2 units down, so:

[tex]k=1 \\ \\ c=2 \\ \\ \\ Finally: \\ \\ g(x)=log(x-1)-2[/tex]

Below you can see the graph. The red one is the original function while the blue one is the translated one.

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Answer:

B

Step-by-step explanation:

Took test on edge

Answer:

The percent (relative) change is 7.14 percent (%).

Step-by-step explanation:

We are given that the original support value is at 42%.

Then the support increased by 3%, to reach 45%.

We want the Percentage Change (i.e. relative) change of this increase, which can be computed as:

[tex]\frac{X_{F}-X_{O}}{X_{O}}*100[/tex]

where [tex]X_{F}[/tex] is the final value reached

           [tex]X_{O}[/tex] is the original value

So plugging in our known values and computing we have:

[tex]\frac{45-42}{42}*100= \frac{3}{42}*100 = 0.071428*100=7.14[/tex] percent increase.

Now lets go back and check if we are correct.

[tex]42+42\frac{7.14}{100}=42+2.9988=42+3=45[/tex]

So it works!

Answer:

-50/7

Step-by-step explanation:

-7 1/7=-50/7

Because 7*7+1=49+1=50, and don't forget the negative sign.

Answer:

π = a/(r²) = a÷(r²)

Answer:

pie is equal to the square root of A divided by r

Step-by-step explanation:

Set the equation first...a=pie times r squared. Then u need to get rid of everything to make pie by itself. U square both sides or all the equation. the square cancels out and on the other side, it will be the square root of a. Next, divide by r on each sides. The r cancels out. Then it's gonna be pie =the square root of a all over r. It can't be a/r square because in the original...pie is being multiplied by r which is squared so that means both variables are squared. U cant find pie if the square is stopping it so u square for the very first step

Answer:

53/50

Step-by-step explanation:

The ratio of males to females is 53:50.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Number of baby boys = 106

Number of baby girls = 100

So, the ratio of males to females

= 106/100

= 53/50

Hence, the ratio of males to females is 53:50.

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The solution of given inequality is: [tex]x>-3[/tex]

Solution:

Given inequality is:

[tex]7(x+1)>-14[/tex]

We have to find the value of "x"

Let us solve the given inequality

Divide both sides of inequality by 7

[tex]\frac{7\left(x+1\right)}{7}>\frac{-14}{7}\\[/tex]

Simplify the above expression

[tex](x+1)>-2[/tex]

[tex]x+1>-2[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides\: of\: inequality}[/tex]

[tex]x+1-1>-2-1\\\\x>-3[/tex]

Thus the value of x is [tex]x>-3[/tex]

The complete question is:

A geometric sequence is defined recursively by

    [tex]a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}[/tex]

(a) Write out the first four terms of this sequence.

(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.

Answer:

Explanation:

You are given the first term,    [tex]a_(1)=40[/tex] , and the recursive formula

   [tex]a_{(n)}=(-1/2)a_{(n-1}[/tex]

Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).

(a) First four terms of the sequence

[tex]a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5[/tex]

Those are the first four terms.

(b) 9th term

You can write the explicit formula of the sequence as:

[tex]a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}[/tex]

Thus, for the 9th term, n = 9, and the term is:

[tex]a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526[/tex]

Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.

Answer:

36

Step-by-step explanation:

If you see this kind of problem do this two steps:

1. Multiply the numerator and the multiplier.

2. Divide the result with the denominator.

[tex]\frac{3}{10}[/tex] × 120

3 × 120 = 360 (STEP 1)

360 ÷ 10 = 36 (STEP 2)

Answer:

36

Step-by-step explanation:

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