All categories

2 years ago

Find a26 in the arithmetic sequence: -15, -35, -55, -75

Mathematics

1 answer:

MrRissso [65]2 years ago

4 0

Answer: x=−5

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4−7x=31

−4+−7x=31

−7x−4=31

Step 2: Add 4 to both sides.

−7x−4+4=31+4

−7x=35

Step 3: Divide both sides by -7.

−7x

−7

x=−5

You might be interested in

There are 220 students in Year 7. 15% cycle to school. 60% are driven to school. The rest walk to school. (a) How many students

Paha777 [63]

Answer:

cycle=33 students, driven=132 students, walk=55 students

Step-by-step explanation:

<h2>solution</h2><h2>60+15+x=100 to get the remaining percentage</h2><h2>x=25</h2><h2>15÷100×220=33</h2><h2>60÷100×220=132</h2><h2>25÷100×220=55</h2>

7 0

1 year ago

Read 2 more answers

Drew earns money washing cars for his neighbors on the weekends. Drew charges a set rate for each car he washes.

statuscvo [17]

Answer:

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

$F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)$

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$

The magnitude force will be

$|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68$

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

$\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469$

The angle formed by F and y axis

$\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=$

The angle formed by F and z axis

$\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359$

8 0

2 years ago

Erik drives 19.2 miles in 16 minutes.

Kipish [7]

Bruh it clearly says 65 mph so that’s the answer

7 0

2 years ago

Last year Ron bought 40 pen sets and sold 25. This year he bought 75 pen sets and sold 60. The absolute error each year was the

vagabundo [1.1K]

Answer:200

Step-by-step explanation:

5 0

1 year ago

Read 2 more answers