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Dimas [21]
3 years ago
14

Solve for x Need help with this last question

Mathematics
1 answer:
Serhud [2]3 years ago
6 0

Answer:

x = 8

Step-by-step explanation:

2(78°) = 20x - 4

156 = 20x - 4

add 4 to each side of the equation:

160 = 20x

divide both sides by 20:

x = 8

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Daniel has $100. After he buys 4 pencils and 3 pens, he has $7 left. If each pencil costs $3 more than each pen, is $25 enough t
amm1812

Answer:  Yes, Daniel has enough money to buy 2 pens.

=========================================================

Explanation:

x = cost of one pencil

y = cost of one pen

4x = cost of 4 pencils

3y = cost of 3 pens

4x+3y = cost of 4 pencils and 3 pens

100 - (4x+3y) = amount Daniel has left = 7 dollars

100-(4x+3y) = 7 is one equation we can form

Another equation we can form is x = y+3 because "each pencil costs $3 more than each pen".

Let's plug that into the first equation and solve for y.

100-(4x+3y) = 7

100-(4(y+3)+3y) = 7

100 - (4y+12+3y) = 7

100 - (7y+12) = 7

100 - 7y - 12 = 7

-7y + 88 = 7

-7y = 7-88

-7y = -81

y = -81/(-7)

y = 11.57 is the cost of one pen

2y = 2*11.57 = 23.14 is the cost of two pens.

Since this is less than $25, this means he has enough to buy two pens. This assumes that we either ignore tax, or the tax is already included in the listed prices.

5 0
2 years ago
X² + 3x -4 = 0<br> Factor the quadratic equation
guajiro [1.7K]

Answer:

(x-1)(x+4)

Step-by-step explanation:

x^2+3x-4\\x^2-x+4x-4\\x(x-1) 4(x-1)\\(x-1)(x+4)

4 0
3 years ago
Read 2 more answers
What is an equation of the line perpendicular to y=-x-2 and through (-2, 4)?
Salsk061 [2.6K]

Answer: y = x + 6

Step-by-step explanation:

\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:perpendicular\:to\:}y=-x-2\mathrm{\:that\:passes\:through\:}\left(-2,\:4\right)

\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}

m=-1

\mathrm{The\:perpendicular\:slope\:is\:the\:negative\:reciprocal\:of\:the\:given\:slope}

\left(-1\right)m_p=-1

\frac{\left(-1\right)m_p}{-1}=\frac{-1}{-1}

m_p=1

\mathrm{Compute\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:for\:slope\:m=}1\mathrm{\:and\:passing\:through\:}\left(-2,\:4\right)\mathrm{Plug\:the\:slope\:}1\mathrm{\:into\:}y=mx+b

y=x+b

\mathrm{Plug\:in\:}\left(-2,\:4\right)\mathrm{:\:}\quad \:x=-2,\:y=4

4=\left(-2\right)+b

-2+b=4

\mathrm{Add\:}2\mathrm{\:to\:both\:sides}

-2+b+2=4+2

\text{Simplify}

b=6

\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=1\mathrm{\:and\:}\mathbf{b}=6

y=x+6

3 0
3 years ago
John recieves £173 per week after working for 25 hours. How much does he get per hour
inessss [21]

Answer:

Amount John gets paid per hour 6.92 Dollars per hour ,

Step-by-step explanation:

To find how much he gets paid per hour we need to divide the total payment he received by the total number of hours he worked.

Amount John gets paid per hour = \frac{173}{25} Dollars per hour.

                                                       =6.92 Dollars per hour

4 0
4 years ago
On the left, prism A. Prism A is a triangular prism. The base has side lengths of 6 centimeters, 8 centimeters, and 10 centimete
Llana [10]

Answer:

Prism B has a larger base area

Step-by-step explanation:

Given

Base dimensions:

Prism A:

Lengths: 6cm, 8cm and 10cm

Prism B:

Lengths: 5cm and 5cm

Required [Missing from the question]

Which prism has a larger base area

<u>For prism A</u>

First, we check if the base dimension form a right-angled triangle using Pythagoras theorem.

The longest side is the hypotenuse; So:

10^2 = 8^2 + 6^2

100 = 64 + 36

100 = 100

The above shows that the base dimension forms a right-angled triangle.

The base area is then calculated by;

Area = 0.5 * Products of two sides (other than the hypotenuse)

Area = 0.5 * 8cm * 6cm

Area = 24cm^2

<u>For Prism B</u>

Lengths = 5cm\ and\ 5cm

So, the area is:

Area = 5cm * 5cm

Area = 25cm^2

<em>By comparison, prism B has a larger base area because </em>25cm^2 > 24cm^2<em></em>

5 0
3 years ago
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