Solving exponential equations with the same base
Solve for x:
(-3)* = (-3) 13
O 13
Ox+13
0-3
Ox-13

The value of x and y for the given set of triangle is x = 1.8022 cm and y = 0.9054 cm.

In geometry, a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry and has many properties and applications in mathematics and other fields. The sum of the interior angles of a triangle is always 180 degrees, and the area of a triangle can be calculated using various formulas depending on the given information, such as the base and height, the lengths of the sides, or the angles. Triangles can also be classified based on the length of their sides and the measure of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are used in many fields, including engineering, architecture, physics, and computer graphics, among others.

Here,

We can use the Pythagorean theorem and the fact that the base is divided by the altitude in a 3:1 ratio to find x and y.

Let's call the length of the altitude h, and the length of the base b.

Since the base is divided by the altitude in a 3:1 ratio, we have:

b/h = 3/1

b = 3h

We know that the side adjacent to the angle is 6 cm, and that the height of the altitude is x cm. Therefore, we have:

cos(θ) = adjacent/hypotenuse

cos(θ) = 6/b

cos(θ) = 6/(3h)

cos(θ) = 2/h

We also know that the length of the altitude is h, and that the length of the base is 3h. Therefore, we have:

h² + (3h)² = (6 cm)²

Simplifying this equation gives:

h² + 9h² = 36

10h² = 36

h² = 3.6

h = √(3.6)

h = 1.8974 cm (rounded to four decimal places)

Now we can use the equation we derived earlier for cos(theta) to find y:

cos(θ) = 2/h

cos(θ) = 2/1.8974

cos(θ) = 1.0546 (rounded to four decimal places)

y = hypotenuse * sin(θ)

y = 6 * sin(cos⁻¹(1.0546))

y = 0.9054 cm (rounded to four decimal places)

Therefore, x = √(h² - y²)

= √(3.6 - 0.9054²)

= 1.8022 cm (rounded to four decimal places)

So, x = 1.8022 cm and y = 0.9054 cm.

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Answer:

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

The triangle with sides 3, 6 and y is a special 30°×60°×90° right triangle as one of the legs is half the length of the hypotenuse.

It has a property, ratio of sides:

Substitute values for a = 3and c = 6 to get:

It gives us the value of y:

The triangle with sides x and y is also a specific 30°×60°×90° right triangle with y being the short leg, hence the ratio of its sides is:

Substitute the value of y and solve for x:

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

There is another solution:

Step 1. Use Pythagorean theorem to find the value of y:

Step 2. Use the geometric mean theorem to find the value of x:

The surface area of the rectangular prism is 368 square centimeter.

Given that, dimensions of the rectangular prism are length=14 cm, width=5 cm and height=6 cm.

We know that, the surface area of the rectangular prism = 2lw+2lh+2hw.

Here, the surface area = 2×14×5+2×14×6+2×6×5

= 368 square centimeter

Therefore, the surface area of the rectangular prism is 368 square centimeter.

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Answer:

1) 4

2) 6

3) 10

4) 30°

5) 48°

6) 55°

7) 68°

8) 148°

9) 102°

10) 48°

The correct answer choices for the complementary angles as well as congruent angles  are:

Complementary angles are two angles that when they are summed up give the sum of 90 degrees (90°).

The complementary angle in the given question is as follows:

5 and 6 since their sum are 90 degrees.

Congruent angles are two or more angles that are equal in size.

An example of congruent angles from the given question is 8 and 10 since they are vertically opposite angles.

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The height of the square pyramid is 58.95 units.

To find the height of the square pyramid, we can use the Pythagorean theorem. Let's call the height "h".

The slant height is the hypotenuse of a right triangle with legs equal to half the length of one side of the square base and the height of the pyramid. The length of one side of the square base is given as 22, so the length of half a side is 11. Using the Pythagorean theorem, we get:

[tex]h^{2}[/tex] + [tex]11^{2}[/tex] = [tex]60^{2}[/tex]

Simplifying, we have:

[tex]h^{2}[/tex]  + 121 = 3600

Subtracting 121 from both sides, we get:

[tex]h^{2}[/tex]  = 3479

Taking the square root of both sides, we get:

h ≈ 58.95

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Answer: m=6.2, direction is 57.84 degrees north of east

Step-by-step explanation:

Break up each into x and y parts of the vector

first part only has a y

<0, 4.5>

2nd <2, 0>

3rd  use trig

sin 30 = y/1.5

y=.75

cos30 =x/1.5

x=1.3

<1.3, .75>

Add all x's and y's

<3.3, 5.25>   to find magnitute use pythagorean

m²=3.3²+5.25²

m=√38.45

m=6.2

to find direction use trig again

tan∅=5.25/3.3

∅=57.84

The annual percentage rate is 6.81%.

What is compound interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.

Principal = $1135

Total Amount = $132.51 * 9 = $1192.59

Time = 9 months = 9/12 years = 0.75 years

Now using compound interest formula,

=> Amount =[tex]P(1+r)^n[/tex]

=>[tex]$1192.59 = $1135 * (1+r)^{0.75[/tex]

=>[tex](1+r)^{0.75 = 1.0507[/tex]

Taking log both sides , we get ,

=> 0.75 ln(1+r) = ln(1.0507)

=> 1 + r = e0.0659

=> 1 + r = 1.0681

=> r = 0.0681

rate = 6.81%

Hence the annual percentage rate is 6.81%.

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The area of the shaded region is 47.1 units²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of the shaded region = area of big sector - area of small sector

area of a sector is expressed as;

A = (tetha)/360 × πr²

Area big sector = 40/360 × 3.14 × 12

= 18.086.4/ 360

= 50.24 units²

Area of small sector =

40/360 × 3.14 × 3²

= 1130.4/360

= 3.14 units²

Area of the shaded region = 50.24 - 3.14

= 47.1 units²

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A.= [tex]$\left( -4,\frac{5\pi}{4}\right)\,\, \left( 4,\frac{-7\pi}{4}\right)[/tex],  B = [tex]$\left( 4,\frac{3\pi}{4}\right)\,\, \left( -4,\frac{-\pi}{4}\right)[/tex],

C=[tex]$\left( -4,\frac{\pi}{4}\right)\,\, \left( 4,\frac{5\pi}{4}\right)[/tex],  D = [tex]$\left( -4,\frac{3\pi}{4}\right)\,\, \left( 4,\frac{7\pi}{4}\right)[/tex]

[tex]$\left( -4,\frac{5\pi}{4}\right) = \left( 4,\frac{5\pi}{4}+\pi = 2\pi + \pi/4\right )\,\,, \left( 4,\frac{-7\pi}{4}\right) =\left( 4,\frac{-7\pi}{4}+2\pi = \pi/4\right)[/tex]

[tex]$\left( 4,\frac{3\pi}{4}\right)\,\, , \,\left( -4,\frac{-\pi}{4}\right) = \left(4,\frac{-\pi}{4}+\pi = 3\pi/4\right)[/tex]

[tex]$\left( -4,\frac{\pi}{4}\right)=\left( 4,\frac{\pi}{4}+\pi = 5\pi/4\right)\,\, ,\,\left( 4,\frac{5\pi}{4}\right)[/tex]

[tex]$\left( -4,\frac{3\pi}{4}\right)=\left ( 4,\frac{3\pi}{4}+\pi = 7\pi/4 \right)\,,\, \left( 4,\frac{7\pi}{4}\right)[/tex]

When [tex]r\geq 0[/tex] and [tex]0\leq \theta < 2\pi[/tex], we call the polar coordinates [tex](r,\theta)[/tex] standard polar coordinates. To convert any given coordinates to standard coordinates 1. if r<0 then replace r with |r| and [tex]\theta[/tex] with [tex]\theta + \pi[/tex]. 2. Now if [tex]\theta < 0 \textrm{ or }\theta\geq 2\pi[/tex], we add a suitable multiple of [tex]2\pi \textrm{ to }\theta[/tex] to bring it inside [0,[tex]2\pi[/tex]) interval.

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The area of the figure ABCDE is 24648 square cm

From the question, we have the following parameters that can be used in our computation:

The figure

Start by calculating the height of the triangle using

tan(61) = h/80

So, we have

h = 80 * tan(61)

h = 144.32

The area is then calculates as

Area = Sum of individual areas

So, we have

Area = 1/2 * 144.32 * 80 + 160 * 60 + 110 * (144.32 - 60)

Evaluate

Area = 24648

Hence, the area is 24648

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Answer:

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

First determine the interest and then use the formula for ordinary interest.

Calculate the interest:

Use the ordinary interest formula:

Plug in the values and solve for Time:

Isolate the Time variable:

Tara would have to pay back the loan in approximately 120 days.

Given ΔABC, the measure of b include the following: D. b = 11.690 units.

In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

a + c + b = 180°

53 + 58 + b = 180°

b = 180° - 111

b = 69°

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

sin69/b = sin53/10

b = 10sin69/sin53

b = 11.690 units.

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The number in the given expression is 160.

We have,

Let's call the number "x".

The difference between twice a number and its half is:

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

One-fifth of this difference is 24, so we can set up the equation:

(1/5)(3/2)x = 24

Multiplying both sides by 10 to eliminate the fraction, we get:

3x = 480

Dividing both sides by 3, we get:

x = 160

Therefore,

The number in the given expression is 160.

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The complete question.

One fifth of the difference between twice a number and its half is 24. What is the number.

Answer:

[tex] \frac{7x - 11}{20} = \frac{4x - 2}{15} [/tex]

[tex]15(7x - 11) = 20(4x - 2)[/tex]

[tex]105x - 165 = 80x - 40[/tex]

[tex]25x = 125[/tex]

[tex]x = 5[/tex]

ABC  Company has sales forecasts of the following .cash receipts for March are $45,820

What is calculation?.

The calculation involves applying the given collection percentages to the sales forecasts and then subtracting the uncollectible percentage from the total amount of sales. The calculation steps are as follows:

Calculate the amount of January sales that will be collected in March: $40,000 x 0.20 = $8,000

Calculate the amount of February sales that will be collected in March: $65,000 x 0.50 = $32,500

Calculate the amount of March sales that will be collected in March: $52,850 x 0.25 = $13,212.50

Add up the three amounts of collections: $8,000 + $32,500 + $13,212.50 = $53,712.50

Calculate the uncollectible amount: $157,850 x 0.05 = $7,892.50

Subtract the uncollectible amount from the total collections: $53,712.50 - $7,892.50 = $45,820

Therefore, the calculation shows that the cash receipts for March are $45,820.

To calculate the cash receipts for March, we need to first determine how much of the January, February, and March sales will be collected in March.

For January sales, 20% will be collected in March, which is $40,000 x 0.20 = $8,000.

For February sales, 50% will be collected in March, which is $65,000 x 0.50 = $32,500.

For March sales, 25% will be collected in March, which is $52,850 x 0.25 = $13,212.50.

To account for the 5% uncollectible, we need to subtract 5% of the total amount of sales from the total cash receipts. The total sales are $40,000 + $65,000 + $52,850 = $157,850. So, 5% of $157,850 is $7,892.50.

Therefore, the total cash receipts for March are:

$8,000 + $32,500 + $13,212.50 - $7,892.50 = $45,820

The cash receipts for March are $45,820

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Answer:

The other two angles are 22° , 22°

Step-by-step explanation:

To find the other angles, we can use angle sum property of triangle.

      The given angle 136° cannot be base angles. Let the base angles be x.

x + x + 136 = 180°

   2x + 136 = 180°

Subtract 136 from both sides,

            2x = 180 - 136

            2x = 44°

Divide both sides by 2,

              x = 44 ÷ 2

                [tex]\sf \boxed{x = 22^\circ}[/tex]

Answer:42

Step-by-step explanation:

The value of test statistic is -2.23.

What is test statistic?

In statistics, a test statistic is a value calculated from a sample of data that is used to assess the evidence against a null hypothesis.

We can use a one-sample t-test to test the hypothesis:

Null hypothesis: The true population mean cost of weddings is $25,549

Alternative hypothesis: The true population mean cost of weddings is less than $25,549

The test statistic can be calculated using the formula:

t = ([tex]\bar{x}[/tex] - μ) / (s / √n)

where [tex]\bar{x}[/tex] is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (24,342 - 25,549) / (5054 / √60) = -2.23

Rounding to two decimal places, we get t = -2.23.

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Answer:

5x^2

Step-by-step explanation:

just is, trust me

Tom and Keira will owe $182,002 in federal income tax for 2022.

To calculate the federal income tax that Tom and Keira will owe in 2022, we need to first determine their taxable income.

Assuming that Tom and Keira have no dependents, their standard deduction for 2022 is $25,900. Therefore, their taxable income is:

Taxable income = Combined income - Standard deduction

Taxable income = $208,264 - $25,900

Taxable income = $182,364

To determine their federal income tax, we need to use the tax brackets and rates for 2022. According to the IRS, for married filing jointly status, the tax rates for 2022 are as follows:

10% on taxable income up to $21,450

12% on taxable income over $21,450 up to $87,850

22% on taxable income over $87,850 up to $183,250

24% on taxable income over $183,250 up to $351,600

32% on taxable income over $351,600 up to $431,200

35% on taxable income over $431,200 up to $666,450

37% on taxable income over $666,450

To calculate the federal income tax owed, we need to apply the appropriate tax rates to the corresponding income brackets. In this case, the taxable income falls within the following brackets:

$21,450 at 10% = $2,145

($87,850 - $21,450) at 12% = $7,026

($183,250 - $87,850) at 22% = $24,457

($351,600 - $183,250) at 24% = $42,336

($431,200 - $351,600) at 32% = $25,280

($666,450 - $431,200) at 35% = $80,758

($182,364 - $666,450) at 37% = $0

Therefore, the total federal income tax owed for 2022 is:

Total federal income tax = $2,145 + $7,026 + $24,457 + $42,336 + $25,280 + $80,758 + $0

Total federal income tax = $182,002

Therefore, Tom and Keira will owe $182,002 in federal income tax for 2022.

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Answer:

For all answers: x = -17, y = -19, (-17,-19)

Step-by-step explanation:

Substitution:

We plug x = y+2 into the second equation

[tex]-2(y+2)+y=15\\-2y-4+y=15\\-y-4=15\\y=-19[/tex]

Plugging back into x = y+2 we get that x = -17

Elimination:

We move y to the other side in Equation 1 and then subtract y.

[tex]x-y=2\\-2x+y=15\\-x=17\\x=-17\\y=-19[/tex]

Plugging X into x-y = 2 we get that y = -19

What method you prefer is up to you

Answer:

Step-by-step explanation:

The missing values in the table are:

Distance 800 m 1200 m

Time Taken _______ _______
The time taken to walk 800m in Table 2 is not provided, so the blank space remains unfilled.

The statement applies on Yuri's budget are

We have,

Yuri earned $51,790 and spent $52,510.

So, after spending the amount of $52, 510 the amount will be

= 51, 790 - 52, 510

= - $720

Here the negative number shows that Yuri was in debt.

Also, the positive integers represent the Earnings.

So, the statement applies on Yuri's budget are

Yuri was in debt by the end of that year.

A positive number should represent Yuri's earnings.

A negative number should represent Yuri's spending.

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The surface area of the prism is 469 in²

The net of the object is a rectangle that is 28 inches long and 14 inches wide. Its area is 392 square inches.

In addition, there are two triangles with a base of 11 inches and height of 7 inches. Together, they have the total area of a rectangle 7 * 11 = 77 square inches.

Therefore, the total surface area of the prism will be the sum of the area of a rectangle and two triangles. i.e

(392 + 77) in² = 469 in²

Hence, the total surface area is 469in².

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Based on the bar chart, there are 5 eels fewer that Angelfish.  

The bar chart shows that there is a total of 25 Angelfish and 20 Eels.

To the difference between both is


25-20= 5 Thus, based on the information presented n the bar chart, there are 5 eels fewer than Angelfish.  

A bar chart is used to display a distribution of data points or to compare metric values across different subgroups of your data.

A bar chart shows which groups are highest or most prevalent, as well as how other groups compare to one another.

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Full question:

See attached graph.

Answer:

When Jordan Reeves was 10 years old, she designed a toy especially for kids who had only one hand, like her. Later, she thought that other kids with physical differences might want to make something familiar. This idea motivated Jordan to start an organization where kids could get creative. The organization's experts conducted design workshops, and the kids who took part benefited in many ways. For instance, the kids learned about the design process, which could help them prepare for jobs later on.

Hope it helps:)

The radical expression √(3x + 12) − 1 = √(5x + 9) when solved for x has a solution of x = -1

From the question, we have the following parameters that can be used in our computation:

√(3x + 12) − 1 = √(5x + 9)

The above equation can be solved using trial by error method

Set x = -1

So, we have

√(3(-1) + 12) − 1 = √(5(-1) + 9)

Evaluate

2 = 2

The above equation is true for x = -1

Hence, the solution is x = -1

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Answer:

Step-by-step explanation:

First mulitply the current salary by 11.5% to find the increase.

Change 11.5% into a decimal by moving the decimal two places to the left.

11.5% becomes .115.

22000 × .115 = 2530 - the increase

22000 + 2530 = 24530 GBP

The new gross salary.

Answer: 125

Step-by-step explanation:

V=lwh

=(5)(5)(5)

=125