The area of the triangle below is sq. units.
3
22

The logarithm base 10 of the number 10 is 1

We have to find logarithm base 10 of number 10.

Therefore, using logarithm rule

logₐ a = 1

Hence,

log₁₀ 10 = 1

Therefore, logarithm base 10 of the number 10 is 1

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Answer:

1

Step-by-step explanation:

Using proportions, it is found that the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each lb has 0,0005 tons. Hence the total weight in tons that we want to put in the elevator is:

T = (175 + 240 + 80 x 50) x 0.0005 = 2.2075 tons.

Hence, the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.

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Answer:

could u send a photo please

98% confidence interval for the mean rate = [4.1437 , 4.4983]

We are given the interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day ;

4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414

Now, Firstly we will find the Mean of the above data, Xbar ;

Mean, Xbar = ∑ x ÷ n =

4.751 + 4.373 + 4.177 + 4.676 + 4.425 + 4.228 + 4.125 + 4.251 + 3.951 + 4.192 + 4.291 + 4.414 ÷ 12 = 4.321

Standard deviation, s = √ ∑(x - x bar)²÷ n-1 = 0.226.

Now, the pivotal quantity for the 98% confidence interval for the mean rate is;

P.Q = x bar - ц ÷ n - 1 ≈ tn - 1

where, Xbar = sample mean

s = sample standard deviation

n = sample size = 12

So, 98% confidence interval for the mean rate, μ is ;

P(-2.718 < t₁₁ <2.718) = 0.98

P(-2.718 <Xbar - μ σ√ⁿ < 2.718) = 0.98

P(Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar +  2.718 * ₈÷ √ⁿ ) = 0.98

98% confidence interval for μ = (Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar +  2.718 * ₈÷ √ⁿ ) = 0.98

[4.321 - 2.718 * 0.226 ÷ √₁₂ , 4.321 + 2.718 * 0.226 ÷ √₁₂

                                  = [4.1437 , 4.4983]

Therefore, 98% confidence interval for the mean rate = [4.1437 , 4.4983]

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By using the concepts of relations and functions and based on the table given, the function presents the following relationship:

x → f(x)

7 → 95

Functions are relations between an input set named domain (x) and an output set named range (f(x)), that is:

x → f(x)

After a quick observation, for x = 7, then f(7) = 95. In more graphically manner, the function present the respective relation:

7 → 95

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The value of the expression when evaluated is: 162.

To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.

6(-1^4) × 3^3

6(1) × 27

6 × 27

162

The value of the expression, 6x^4y^3, is: 162.

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Donna sold 3 pencils and 8 pens solved using simultaneous equation

What is a simultaneous equation?

Simultaneous equation refers to related equations that are solved at the same to derive answers to the unknown variables

Let assume that X pencils were sold and Y pens were sold

The total revenue is the sum of the prices multiplied by the quantities sold.

2X+3Y=30   (equation 1)

The sum of X and Y sold is 11

X+Y=11   (equation 2)

multiply the second equation by 2

2*(X+Y=11)

2X+2Y=22 (equation 3)

subtract equation 3 from 1

(2X+3Y=30)-(2X+2Y=22)

Y=8

Substitute for Y in equation 2

X+8=11

X=11-8

X=3

Which means he sold 3 pencils and 8 pens.

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Answer:

8

Step-by-step explanation:

Answer:

jupiter, Saturn, Uranus, neptune are all distance from sun

Step-by-step explanation:

Answer:

AU:

Merc-0.39

Venus-0.72

Earth- 1

Mars- 1.52

Jupiter - 5.20

Uranus - 19.1

Neptune - 30

Years:

Merc-0.24

Venus-0.61

Earth- 1

Mars- 1.88

Uranus - 84?(maybe)

Neptune - 165

Step-by-step explanation:

Edge

Answer:

x=9

Step-by-step explanation:

3/4x+2 1/4=9

3/4x=9-2 1/4

3/4x=6 3/4

4(3/4x)=4(6 3/4)

3x=27

x=9

Answer:

x = 9

Step-by-step explanation:

3/4 x + 2 1/4 = 9      subtract 2 1/4 from both sides of the equation

3/4  x = 6 3/4           now divide both sides by 3/4

x = 9

The largest possible error in the area of the circle is of 44%.

The area of a circle of radius r is given by:

[tex]A = \pi r^2[/tex]

With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:

[tex]A = \pi \times 10^2 = 100\pi[/tex]

With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:

[tex]A = \pi \times 12^2 = 144\pi[/tex]

The error is given by:

[tex]E = 144\pi - 100\pi = 44\pi[/tex]

The percent error is the error divided by the initial amount, multiplied by 100%, hence:

[tex]P = \frac{44\pi}{100\pi} \times 100\% = 44\%[/tex]

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Answer:

0.1359

Step-by-step explanation:

For the function f(x) = 4|x - 3| + 4, we have that:

The x-intercept of a function is the value of x when y = f(x) = 0, hence:

0 = 4|x - 3| + 4

4|x - 4| = -4

|x - 4| = -1

The absolute value cannot be negative, hence the function has no x-intercepts.

The x-intercept of a function is the value of y = f(x) when x = 0, hence:

f(0) = 4|0 - 3| + 4 = 12 + 4 = 16.

The y-intercept is of y = 16.

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Answer:

E

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m = [tex]\frac{4-1}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1

using (a, b ) = (3, 4 ) , then

y - 4 = 1 (x - 3) → E

The reportable square footage for Kinsey's home = 2150square feet.

The main floor of Kinsey's home is 1,425 square feet.

The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.

The finished basement is 1,425 square feet with 7.5-foot ceilings.

That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).

Kinsey should report square feet (1425+875- 150)

= 2150square feet.

Hence, The reportable square footage for Kinsey's home = 2150square feet.

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Answer:

108 km/hr

Step-by-step explanation:

45 minutes = 3/4 hours

1) Distance = speed × time

= 60 × 3/4

= 45 km

2) 20 minutes = 1/3 hours. So, 3/4 - 1/3 = 5/12 hours.

speed = distance / time

= 45 / 5/12

= 108 km/hr

a. Find the graph in the attachment

b. As h increases, e tends to 90°

Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.

The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.

To plot the graph, we see that the function is the tangent function.

The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°

Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞

So, we plot h = 22tane for 0 ≤ e ≤ 90°

Find the graph in the attachment

From the graph, we seet that at high h or as h increases, e tends to 90°

So, as h increases, e tends to 90°

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Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be 7.01 billion.

To calculate the percentage increase rate, use the fundamental increase charge formulation: subtract the original from the brand new cost and divide the results by way of the original cost. to show that right into a percent boom, multiply the results by 100.

The population of a given area is described as the range of humans generally residing in that vicinity, measured on 1 January in a given 12 months. The supply can be the most latest population census.

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Answer:

cocomelon . 3/5 - 4

Step-by-step explanation:

Answer:

x=[tex]\sqrt3[/tex] and -[tex]\sqrt3\\[/tex]

Step-by-step explanation:

the roots(zeros) are the value of x where the graph intersects the x-axis.

to find the roots:

x^2-3=0

x^2=3

x=+-[tex]\sqrt3[/tex]

Answer:

16 Liters of the correct answer.

Emil started his lemonade stand with 12 litres of Lemonade.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon.

When he closes for the day, he has 4 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.

x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4

x - ( x/2) - (x/8) - ( x/24) = 4

[ 24x -12x -3x - x][24] = 4

8x  =  96

x = 12 liters

Therefore Emil started his lemonade stand with 12 liters of Lemonade.

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Answer:

36 units

Step-by-step explanation:

to do this you must first find the lengths of all the sides with pythagorean theorem

for a to b you use

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

c = 5

5 is one of the lengths

b to c uses the same equation

so

5 is another one of the lengths

for d to c your equation is

5^2 + 12^2 = c^2

25 + 144 = c^2

169 = c^2

13 is another of the lengths

d to a has the same length as c to d so there is another 13 unit length

so

5 + 5 + 13 + 13 is your equation to find the perimeter

5 + 5 + 13 + 13 = 36

that is your answer

Answer:

18 degrees

Step-by-step explanation:

Supplementary angles are angles that when added together equal 180 degrees.

A + 162 = 180

     - 162  -162

        A  = 18

Answer:

18

Step-by-step explanation:

When your are asked the supplement you minus 162 from 180. When you join SU from supplement and add a 1 behind SU you'll get 180. [1SU TO 180]

180-162

18

The lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20. This can be obtained by adding um and md which is equal to ud. An equation is obtained and solve for x.

Given that, um=5x+30  

                  md=3x+80

                  ud=10x+20

We know that m is the midpoint of ud

Thus, um + md = ud

                 5x+30 + 3x+80 = 10x+20

                 5x+3x + 30+80 = 10x+20

                      8x + 110 = 10x+20 (taking terms with x to one side of equation)

                             10x - 8x = 110 - 20

                                     2x = 90

                                   ⇒ x = 45

Therefore the lengths,

um=5x+30 = 5(45)+30 = 225 + 30 = 255

md=3x+80 = 3(45)+80 = 135 + 80 = 215

ud=10x+20 = 10(45)+20 = 450 + 20 = 470

Hence the lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20.

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Answer:

(B). F(X)=2x^2+2x-4

Step-by-step explanation:

-4 means it passes through -4 at the y axis

B and D have -4

graph passes thru x axis at -2 and 1

if you enter x = -2 or 1 in the formula

(B). F(X)=2x^2+2x-4

you get 0

it's not D because when you enter -2 or 1 for x

you don't get 0

you get 8 and -4

Answer: (B). F(x) = 2x² + 2x - 4

Step-by-step explanation:

      Let us think about the parent function F(x) = x² to pick our answer.

      Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.

      Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.

Answer:

B) f≥0.2(375,000) +7,200

Step-by-step explanation:

≥ means 'at least'

Answer:

-20

Step-by-step explanation:

-5-5-5-5=-20

Answer: 38.2 degrees

Step-by-step explanation:

[tex]b^2 = a^2 + c^2 - 2ac \cos B\\\\5^2 = 3^2 + 7^2 - 2(3)(7) \cos B\\\\25 = 58-42 \cos B\\\\-42 \cos B=-33\\\\\cos B=\frac{33}{42}\\\\B \approx 38.2^{\circ}[/tex]

Answer:

1, 5

Step-by-step explanation:

-16/4=-4

10/5=2

1/2=1/2

-1/-3=1/3

-1/4/1/2=-1/2

The negative ones are your answer.

Answer: Option D

[tex]\displaystyle d=\frac{C}{\pi}[/tex]

Step-by-step explanation:

    To solve the formula for d, we will isolate the d variable.

  Given:

C = πd

  Divide both sides of the equation by π:

[tex]\displaystyle\frac{C}{\pi}=\frac{\pi d}{\pi}[/tex],     [tex]\displaystyle\frac{C}{\pi}=d[/tex]

  Reflexive property

[tex]\displaystyle d=\frac{C}{\pi}[/tex]

The statements about the function that are true include:

g(0) = 0

g(1) = -1

g(-1) = 1

From the information, the points include:

(x1, y1) = (-2, 2, 5).

(x2, y2) = (0, 0)

(x3, y3) = (2, 3, 5).

It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in the graph.

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Answer:

y = [tex]\frac{7}{6}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )

m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]

• Parallel lines have equal slopes , so

m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line

Hey there!

[tex] \\ [/tex]

[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]

[tex] \\ [/tex]

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .

[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]

[tex] \\ [/tex]

⇒Subtitute the values :

[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]

[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]

[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]

[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:

[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]

[tex] \\ [/tex]

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