Find the value of x in the triangle shown below.
5.7
66

Answer:

He invested $117,000 at 5% interests and  3*117,000 + 23000 = $374,000 at 6% interests

Step-by-step explanation:

Let's call x to the some money at 5% simple interest the actor invest. Then, he invested 3x + 23000 dollars at 6% simple interest.

At 5% simple interest, after one year he earned the following interests:

I = P*r*t

I = x*0.05

At 6% simple interest, after one year he earned the following interests:

I = (3x + 23000)*0.06 = 0.18x + 1380

The total annual interest earned from the investment is $28,290, then:

0.05x + 0.18x + 1380 = 28290

x = (28290 - 1380)/0.23

x = $117,000

Answer:

[tex]x=-30;\quad \:I\ne \:0[/tex]

Step-by-step explanation:

[tex]In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)[/tex]

[tex]\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\[/tex]

[tex]\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:[/tex]

[tex]\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0[/tex]

Answer:

[tex]2x^2+7x+3[/tex]

Step-by-step explanation:

[tex](x+3)(x-7)+(x+8)(x+3)[/tex]

[tex](x^2-4x-21)+(x^2+11x+24)[/tex]

[tex]x^2-4x-21+x^2+11x+24[/tex]

[tex]2x^2+7x+3[/tex]

Answer:

184

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

you do 8x2x4

Answer:3

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

90 - 45 = 45

Answer:I go with A,C,E

Step-by-step explanation:

hope this help

Answer:

$30 to $40

Step-by-step explanation:

387/25= 15.48 (this is how big the tank is)

15.48*2.13= 32.97 (about 33 paying for the highest price)

Sylvie will need approximately 15.48 gallons of gas for her 387-mile trip. With gas prices ranging from $1.95 to $2.13 per gallon, she should plan to spend between $30.20 and $32.96. Therefore, the anticipated cost falls between $30 and $40 that is option B is correct.

To calculate the cost of gas for the trip, we need to follow these steps:

Determine the number of gallons of gas needed for the trip:

Number of Gallons = Total Miles / Miles per Gallon

Number of Gallons = 387 miles / 25 miles per gallon = 15.48 gallons

Calculate the minimum and maximum cost of gas:

Minimum Cost = Number of Gallons * Minimum Price per Gallon

Minimum Cost = 15.48 gallons * $1.95 per gallon ≈ $30.20

Maximum Cost = Number of Gallons * Maximum Price per Gallon

Maximum Cost = 15.48 gallons * $2.13 per gallon ≈ $32.96

Both calculations indicate the cost will fall between $30 and $40. Therefore, the correct answer is: $30 to $40.

Answer:

Area = 80

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Vertical length-16

Horizontal length- 10

make four separate triangles out of the rectangle

each triangle has an area of of 20 (8×5= 40 40/2=20)

multiply by 4

20×4=80

The reflection over the [tex]y-axis[/tex]  then a dilation by the factor of

[tex]\frac{1}{2}[/tex] with a center of dilation at the origin.

Reflecting on the [tex]y-axis[/tex] we get the rectangle A, B, C, D.

A dilation by the factor of [tex]\frac{1}{2}[/tex] with the center of dilation at the origin transforms the rectangle A, B, C, D onto the rectangle A'B'C'D'.

So, the reflection over the [tex]y-axis[/tex]  then a dilation by the factor of [tex]\frac{1}{2}[/tex]  with a center of dilation at the origin.

The image is attached below.

Learn more about the topic reflection of the point:

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The correct sequence of transformations to map rectangle ABCD onto rectangle A'B'C'D' is a dilation by a scale factor of 1/2. This transformation reduces the size of the original rectangle without additional translation, reflection, or rotation.

The correct sequence of transformations that maps rectangle ABCD onto rectangle A'B'C'D' is:

c. a dilation by a scale factor of 1/2

Here's why:

1. A dilation by a scale factor of 1/2 reduces the size of the original rectangle by half. This transformation scales down all the coordinates by a factor of 1/2. Given the coordinates of ABCD and A'B'C'D', this is the only transformation needed to achieve similarity.

Options a and b involve additional transformations (translation and reflection) that are not required to achieve similarity, and option d introduces a rotation which is not a dilation by itself.

Learn more about sequence of transformations here:

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Answer:

The radius of the sphere is 7m

Step-by-step explanation:

Given

Volume of a sphere = 1372π/3 m³

Required

The radius.

The volume of a sphere is calculated using the following formula.

V = 4/3 πr³

Where V = volume of the sphere and r represents it's radius.

By substitution;

1372π/3 = 4/3 πr³

Multiply both sides by 3

1372π = 4πr³

Divide through by 4

343π = πr³

Divide through by π

343 = r³

Take cube root of both sides.

r = 7.

Hence, the radius of the sphere is 7m

Answer:

I believe the answer is B

Step-by-step explanation:

Answer:

The answer is 21

Step-by-step explanation:

The answer is 21 because...

The x-intercept of the graph is (0.3, 0).

The y-intercept of the graph is (0, 0.4).

We have,

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The intercepts are:

The x-intercept is the point of the line when y = 0,

The y-intercept is the point on the line when x = 0.

Now,

Apply the intercepts concept on the given graph.

From the graph,

The point when x = 0 is 0.4.

The point when y = 0 is 0.3.

Thus,

The x-intercept of the graph is (0.3, 0).

The y-intercept of the graph is (0, 0.4).

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Hi

formula. for  circumference of a circle is. : 2πR. if you have the radius.

As the diameter is twice the radius,  then  circumference is. diameter π

then : 18*π≈ 56.52

the mistake was to take the diameter as the radius.

Final answer:

The circumference of the circle is 56.52 m. Eugene made the mistake of using the radius instead of the diameter to calculate the circumference.

Explanation:

The circumference of a circle can be found using the formula C = πd, where C represents the circumference and d represents the diameter.

In this case, the diameter of the circle is given as 18 m. If we substitute this value into the formula, we get:

C = 3.14 * 18 = 56.52 m

Eugene's mistake was that he used the value of the radius instead of the diameter to calculate the circumference. The correct circumference is 56.52 m, not 113.04 m.

Answer:

300 centimeters ( cm)

Step-by-step explanation:

The operation is   "multiply by 100 the numbers of  meters because there are 100 cm in 1 m "

1m=100 cm

3m=3*100 cm=300 cm

There are 100 centimeters in a meter, resulting in 300 centimeters.

The operation needed to convert meters to centimeters is multiplication because there are 100 centimeters in 1 meter. To convert 3 meters to centimeters, you simply multiply 3 meters by the conversion factor of 100 centimeters per meter.

Therefore:

3 meters × 100 centimeters/meter = 300 centimeters

Using this operation and knowing the conversion factor, we find that 3 meters is equal to 300 centimeters.

Answer:

30/80       9/24           6/16

Step-by-step explanation:

Answer:

just multiply a fraction equal to 1 for example 2/2

3/8 x 2/2 = 6/16

3/8 x 3/3 = 9/24

3/8 x 4/4 = 12/32

it is equivalent because 2/2 is equal to 1 so it is being multiplied by 1

Step-by-step explanation:

Answer:

AB = 2 root 13

AC = 4 root 5

Step-by-step explanation:

AB = sqrt[(-4-2)² + (3-7)²]

AB = sqrt(36 + 16)

AB = sqrt(52)

AB = 2sqrt(13)

AC = sqrt[(-8-0)² + (7-3)²]

AC = sqrt(64+16)

AC = sqrt(80)

AC = 4sqrt(5)

sqrt: square root

Answer:

the second one

Step-by-step explanation:

Answer:

2nd one is right

Step-by-step explanation:

Answer:

79.95

Step-by-step explanation:

The first step is to rewrite the percentages into decimals so they can be added or subtracted easier. To turn a percentage into a decimal, remove the percent sign and move the decimal two spaces to the left (in other words, divide the number by 100).

12% becomes -0.12

8% becomes 0.08

Now, let's solve.

79.99 - 0.12 + 0.08

Evaluating 79.99 - 0.12, the equation becomes 79.87 + 0.08.

Evaluating 79.87 + 0.08, we get the final answer, 79.95.

Answer:

Dividing is the inverse (opposite) of Multiplying.

A negative exponent means how many times to divide by the number.

Answer:

There is a power property for negative exponent powers which says that a power with a negative exponent is equal to 1 between the same power, but with a positive exponent. In other words, to convert the exponent from negative to positive, the power is converted to the denominator

Step-by-step explanation:

Answer: 2.8

Step-by-step explanation:

The unit rate of miles per gallon is found by dividing the total miles (150 mi) by the total gallons (10 gal), resulting in a unit rate of A) 15 miles per gallon.

To find the unit rate of miles per gallon when given 150 miles on 10 gallons of gas, we divide the total number of miles driven by the number of gallons of gas used. The calculation is as follows:

Write down the given values: 150 miles (mi) and 10 gallons (gal).

Divide the total miles by the total gallons to find the unit rate: 150 mi ÷ 10 gal = 15 mi/gal.

Therefore, the unit rate is 15 miles per gallon, which is option A: 15 mi per gal.

Answer:

(4,4)

Step-by-step explanation:

Answer:

(4,4). You already know the y value is 4, so you just plug that into the second equation. You'd get 3x-8=4, then 3x=12, then x=4. (x,y)=(4,4)

Answer:

(2,-1)

Step-by-step explanation:

Multiply first equation by 2:

10x + 2y = 18

Subtract the second equation from this so that the 2y terms cancel:

10x - 3x = 18 - 4

7x = 14

x = 2

Plug into first equation to find y:

5(2) + y = 9

10 + y = 9

y = -1

The answer is (2,-1)

Answer:

Reduction scale

Step-by-step explanation:

Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.

So now looking at 1:25, we see it's a reduction scaling because it's fraction is less than unity.

And what 1:25 means is that 1 on paper while the actual size of the object is 25