Solve the problem by writing and solving a suitable system of equations.
A small business takes out loans from three different banks to buy some new equipment. The total amount of
the three loans is $19,000. The first bank offered an interest rate of 16%. The second bank offered a rate of 18%
and the amount borrowed from this bank was $5000 less than twice as much as the amount borrowed from the
first bank. The third bank offered a rate of 15%. The total annual interest was $3050. How much did they borrow
from each bank?
Equations—

Answer: (1,4)

Step-by-step explanation:

The system of equations:

y=5x-1       (1)

y=x+3       (2)

Hence,

5x-1=x+3

5x-1-x=x+3-x

4x-1=3

4x-1+1=3+1

4x=4

Divide both parts of the equation by 4:

x=1

Substitute the value of x=1 into equation (2):

y=1+3

y=4

Thus, (1,4)

Answer:we need a better picture

Step-by-step explanation:I cant since my eyes are bad

The area of the triangle is x + 1 cm², while the area of the rectangle is x cm². Therefore, there is no value of x that makes the areas of both figure equal, because there is no solution to the equation.

A triangle's area = 1/2(base)(height)

A rectangle's area = length × width.

Area of the green triangle = 1/2(x + 1)(2)

Area of the green triangle = x + 1 cm²

Area of the rectangle = x × 1

Area of the rectangle = x cm²

Setting both areas equal, we have:

x + 1 = x

x - x = -1

0 = -1 [not true]

There's no solution or the values of x.

Therefore, we can conclude that there are no values of x for which the areas of both shapes are equal, because there is no solution to the equation.

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The given two triangles ΔQRS and ΔTUV are similar.

What is similar figures?

The same shape between two figures is referred to as similarity. If two figures have congruent corresponding angles and equivalent length ratios on their corresponding sides, they are said to be similar mathematically. The scale factor is the name of this often used ratio.

Given: Two triangles ΔQRS and ΔTUV.

The angles of ΔQRS  are 28°, 76° and 76°.

The angles of ΔTUV are 28°, 76° and 76°.

So, the angles of given two triangles are congruent.

Now consider, the sides of the triangle.

The sides of ΔQRS are, 4, 4, 2 and

The sides of  ΔTUV are 12, 12, 6.

It seems that the sides of the triangle are in proportion.

Therefore, the given two triangles ΔQRS and ΔTUV are similar.

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The amount of time spent on bicycle by Jim =6.5 hours

The amount of time spent on walking by Jim =2.5 hours

To calculate speed, divide the distance travelled by the time it took to complete the voyage, so speed = distance divided by time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.

Distance divided by time equals speed. Distance = time * speed

To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.

Given,

Distance=270miles

Time=9 hours

Speed by walk=4 miles/hour

Speed by cycle=40 miles/ hour

t= time for riding a bicycle

9-t= time for walking

Distance= Speed ×Time

270=40t+4(9-t)

40t+36-4t=270

36t=234

t=6.5

Time spent on bicycle = 6.5 hours

Time spent on walking = 9-6.5

=2.5 hours

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Answer:

53 oranges.

Step-by-step explanation:

To find this, we must set up a proportionality formula.

6                   8

-        =          -

40                 x

Our goal is to find x.

First we cross multiply and get:

6x=320

Now we can divide each side by 6 to get x by itself.

x=53.33,

however, because you cannot have less than a whole orange in a box, each box contained 53.

Step-by-step explanation:

the Hypotenuse (the inclined length of the staircase) of the right-angled triangle is the radius of an imaginary circle with the center at the vertex with the 64°.

then

11 = cos(64) × r

r = 11/cos(64) = 25.09289236...

and

x = sin(64) × r = sin(64) × 11/cos(64) = 11 × tan(64) =

= 22.55334226... ≈ 22.55

△MPQ: M(-4,3), P(-5,8), Q(-1,6). Translation: along (-4,-4) Reflection: in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).

Here we need to find translation along (-4,-4) and reflection in y=x.

First we will find translation,

⇒ (x,y)→ (x-4,y-4)

M(-4,3 )→ M'(-8,-1) ,  

P(-5,8) → P'(-9,4)

Q(-1,6) → Q'(-5,2)  

now we will do reflection,

⇒(x,y) → (y,x)

M'(-8,-1) →  M''(-1.-8)

P'(-9,4) →  P''(4,-9)

Q'(-5,2) → Q''(2.-5).

Therefore translation along (-4,-4) and reflection in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).

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There is 1/6 gallon of milk left in Leo's jug.

The step by step fraction subtraction are as follows:

The first step would be to deduct the 3/4 gallon of milk with 1/3 he uses to make the soup.

3/4 - 1/3 = (3x3)/(4x3) - (1x4)/(3x4) = 9/12 - 4/12 = 5/12

Then out of 5/12 gallon of milk left in the jug, he pours 1/4 of the remaining milk into a glass.

5/12 - 1/4 = 5/12 - (1x3)/(4x3) = 5/12 - 3/12 = 2/12 = (2÷2)/(12÷2) = 1/6

So Leo has 1/6 gallon of milk left in the jug.

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The line is:

y = 400*x + 2000

And the statements are:

The original purchase price of the computer is given by the y-intercept, which is $2,000

The change in the price of the computer is the slope, which is 400.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

Using the graph we can identify two points like:

(1, 1600) and (5, 0)

Then the slope is:

a = (0 - 1,600)/(5 - 1) = 400

And the y-intercept is 2,000, as we can see on the graph.

Then the line is:

y = 400*x + 2,000

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The value of 199.65 rand was worth $24 and $29.11 was worth 243 rand with rounding off.

What is foreign currency exchange?

A global decentralized or over-the-counter market for trading currencies is known as the foreign exchange market. For every currency, exchange rates are set by this market.

Main body:

Given: 1 rand = $0.12

a) According to question ,

199.65 rand = 0.12* 199.65

                    = 23.948

Now rounding off to nearest hundred , we get

199.65 rand = $24

b) According to question,

$1 = 1/ 0.12

$29.11 = 29.11/ 0.12

          =242.5833333

Now rounding off to nearest hundred , we get

$29.11 = 243 rand.

Hence answer are $24 and 243 rand.

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We can use the graph of the line y = 11/7(x) - 58/7 to find the distance between the points

The slope-point equation of a line is given as:

y-y1 = m(x−x1)

where m is the slope of the line, and slope (m) = y2−y1 / x2−x1

Given: the points (-3, -13) and (11, 9)

x1 = -3, y1 = -13 and x2 = 11, y2 = 9

slope(m) = 9-(-13) / 11-(-3) = 22/14 = 11/7

Using y-y1 = m(x−x1), put m = 11/7 and make y the subject:

y-y1 = m(x−x1)

y-(-13) = 11/7(x-(-3))

y + 13 = 11/7(x+3)

y + 13 = 11/7(x) + 33/7

y = 11/7(x) + 33/7 - 13

y = 11/7(x) - 58/7

Therefore, the graph of the line y = 11/7(x) - 58/7 could be used to find the distance between the points

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Answer: The answer is A

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

From trigonometric ratio, we used the tangent of the angle to determine that the flagpole is leaning by an angle of 47.12°

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In the question, we can assume the point of view and the flagpole makes a right angle triangle.

Since we have the opposite and adjacent, we can find the acute angle by using the tangent of the angle

tanθ = opposite / adjacent

tan θ = 14 / 13

θ = tan⁻¹(14/13)

θ = 47.12°

The flagpole is leaning with an acute angle of 47.12 degrees

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His percentage of change in the amount of quarts is 82.22%.

Initial amount of lemonade = 45 quart

End amount of lemonade = 8 quart

Change in amount = 45 - 8

                               = 36

Percent = [tex]\frac{change in value}{initial value}*100[/tex]

             = [tex]\frac{37}{45}*100[/tex]

             = 0.8222 * 100

             = 82.22%

Hence, his percentage of change is 82.22%.

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The slope of line h that is perpendicular to line g is: -4/3.

The slope values of any two lines that are perpendicular to each other are values that are negative reciprocals to each other.

The equation of of line g is given as y = 3/4x + 3/4, it is expressed in slope-intercept form as y = mx + b. This means that the value of the slope of line g is 3/4.

The negative reciprocal of 3/4 is -4/3. Therefore, the slope of line h that is perpendicular to line g would be -4/3.

The slope of line h is: -4/3.

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Answer:

The 3rd answer.

Step-by-step explanation:

2(pi)10 is the equation.

Answer:

y=0.6x+3

Step-by-step explanation:

Slope intercept form: y=mx+b

m- slope

b- y intercept

to find slope with y2-y1/x2-x1

3-0/0-(-5)

3/5

0.6is the slope

y intercept is 3 since it intersects at 3 on the y axis

Hopes this helps please mark brainliest

Answer:10

Step-by-step explanation:Step-by-step explanation:

James's age = x

Jack's age = y

y = 7x

y + 5 = 5(x + 5)

y = 7x

y + 5 = 5x + 25

7x - y = 0

5x - y = -20

7x - y = 0

-5x + y = 20

2x = 20

x = 10

James's age: x = 10

Answer:

-10

-7

-4

Step-by-step explanation:

287 = [tex]a_{1[/tex] + (n-1)3

287 = [tex]a_{1}[/tex]+ (100-1)3

287 = [tex]a_{1}[/tex] + 99(3)

287 = [tex]a_{1}[/tex] + 297  Subtract 297 from both sides

-10 = [tex]a_{1}[/tex]

If the first term is -10  The second term is 3 greater -7 and the third terms is 3 greater than that. -4

When Z=6 and Y=64 the given proportionality value of x = 1/2.

What is proportionality?

  The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount. Two integers that each represent a component of a whole are compared to determine their proportion. In essence, a percentage declares that two fractions are the same even if the amounts are different. For instance, half of 10 marbles is equal to half of 50 marbles in terms of proportion.

Here Z varies jointly as the square root of the product of X and Y.

Then,

=> Z∝[tex]\sqrt{XY}[/tex]

=>Z=k[tex]\sqrt{XY}[/tex]

Where k is constant . Now put X=3 , Y = 12, Z=3.

=> 3=k*[tex]\sqrt{12*3}[/tex]

=> k = 6/3 = 2 .

Then the equation is ,

=> Z==3[tex]\sqrt{XY}[/tex]

Now put Z=6 and Y=64

=> 6 = 3[tex]\sqrt{x*64}[/tex]

=> 2/8 =[tex]\sqrt{x}[/tex]

=>[tex]\sqrt{x}[/tex] = 1/4

=> x = 1/2.

Hence the value of x is 1/2.

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Answer:

0.33=0.33

Step-by-step explanation:

it is answer 0.33=0.33

Answer:$110

Step-by-step explanation:

$100x0.01x10

Answer:

44

Step-by-step explanation:

If a woman has a total of $11,000 to invest. The she invested in each account is: 4000 at 8%, 7000 at 7 %.

Total amount of money invested = $11000

x+y=11000,

Total interest for the year= $760

0.07×x+0.08×y=810

x=11000-y

We substitute for x

0.07×(11000-y)+0.08×y=810

We multiply out

770-0.07y+0.08×y=810

We combine like terms.

0.01×y=40

Divide both side by 0.01y

y = 40 /0.01

y= 4000 at 8%

x=11000-y

Calculate x

x = 11,000 - 4,000

x=7000 at 7 %

Therefore she invested 4000 at 8%, 7000 at 7 %.

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The radius of the circle is 5.91mm

What is the area of the circle?

The area of the circle is the product of mathematical constant pi and square of the radius. radius is the distance of a point on the circle from the center of the circle.

The area of the circle is 110 mm^2

We have to find the radius to do that we first substitute the value of area in the area of circle formula and then compute the value of the radius

We know that,

The area of the circle

= π·r^2

110=22/7*r^2

35 = r^2

r= 5.91mm

Hence The radius of the circle is 5.91 mm

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Answer:

last dagre would be 3

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The degree of a polynomial will be no less than one more than the number of turning points of its graph.

From inspection of the given graph, there are 3 turning points.  

Therefore, the least degree is 4.

The saline concentration of the mixture expressed as a percentage is 42%

A percentage is the expression of a quantity as a fraction that has a denominator of 100.

The volume of the solution that is 30% saline = 80 ml

The volume of the solution that is 90% saline = 20 ml

The concentration of the saline in the mixture; Required;

The table of values can be presented as follows;

Component [tex]{}[/tex] Unit Value [tex]{}[/tex] Amounts (ml) [tex]{}[/tex]  Value

30% saline [tex]{}[/tex]   0.3          [tex]{}[/tex]    80          [tex]{}[/tex]          0.3×80

Solution

70% saline  [tex]{}[/tex]   0.7          [tex]{}[/tex]    20           [tex]{}[/tex]        0.7×20         [tex]{}[/tex]        

solution

Mixture          [tex]{}[/tex]x          [tex]{}[/tex]       100           [tex]{}[/tex]       100 × x

0.3 × 80 + 0.9 × 20 = (80 + 20) × x

42 = 100·x

The concentration of the saline mixture is x = 42/100 = 0.42

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Answer:

B.  37 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where $s$ is the side length.\\\end{minipage}}[/tex]

Given the side length of the square is 4 cm:

[tex]\begin{aligned}\implies \sf Area\;of\;the\;square&=4^2\\&=\sf 16\;cm^2\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where $r$ is the radius. \\\end{minipage}}[/tex]

The radius of a circle is half its diameter.

Given the diameter of the semicircles is 2 cm, then their radius is 1 cm.

[tex]\begin{aligned}\implies \textsf{Area of one semicircle}&= \sf \dfrac{1}{2} \pi (1)^2\\& = \sf \dfrac{1}{2} \pi \; cm^2\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a trapezoid}\\\\$A=\dfrac{1}{2}(a+b)h$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the bases. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given the bases of the trapezoids are 2 cm and 4 cm, and their height is 3 cm:

[tex]\begin{aligned}\implies \textsf{Area of one trapezoid}&= \sf \dfrac{1}{2} (2+4)(3)\\&= \sf \dfrac{1}{2} (6)(3)\\&= \sf (3)(3)\\&=\sf 9\;cm^2\end{aligned}[/tex]

Given the figure is made up of a square, two congruent trapezoids and two congruent semicircles:

[tex]\begin{aligned}\implies\textsf{Area of the figure}&= \sf square+2\;trapezoids+2\; semicircles\\&= \sf 16+2(9)+2\left(\dfrac{1}{2} \pi\right)\\& = \sf 16 + 18 + \pi \\& = \sf 34 + \pi \\& = \sf 37.14159...\; cm^2\end{aligned}[/tex]

Therefore, the measurement that is closest to the area of the figure in square centimeters is 37 cm².

Answer: M = -11/3

Step-by-step explanation: