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9 months ago

Find the indicated length or angle measure (to the nearest tenth).

Mathematics

1 answer:

skad [1K]9 months ago

4 0

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Explain the formula to use

Using the cosine rule which states that:

$z^2=x^2+y^2-2xy\cos Z$

STEP 2: Write the given sides

$x=4,y=6,Z=41^{\circ},z=?$

STEP 3: Find the value of z

$\begin{gathered} By\text{ substitution,} \\ z^2=4^2+6^2-2(4)(6)\cos41 \\ z^2=16+36-48cos41 \\ z^2=52-36.22605985 \\ z^2=15.77394015 \\ z=\sqrt{15.77394015} \\ z=3.971641997 \\ z\approx4.0 \end{gathered}$

Hence, the indicated length is 4.0

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Graph a line with a slope of 1/4 that contains the point (6, 3).

Semenov [28]

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a line in point slope form is

$y-y1=m(x-x1)$

we have

$(x_1,y_1)=(6,3)$

$m=\frac{1}{4}$

substitute

$y-3=\frac{1}{4}(x-6)$

The easiest way to graph a line is to calculate the intercepts

The x-intercept is the value of x when the value of y is equal to zero

For y=0

$0-3=\frac{1}{4}(x-6)$

$-12=(x-6)$

$x=-12+6=-6$

The x-intercept is the point (-6,0)

The y-intercept is the value of y when the value of x is equal to zero

For x=0

$y-3=\frac{1}{4}(0-6)$

$y-3=-\frac{3}{2}$

$y=-\frac{3}{2}+3$

$y=1.5$

The y-intercept is the point (0,1.5)

Plot the intercepts and join the points to graph the line

(-6,0) and (0,1.5)

The graph in the attached figure

8 0

2 years ago

The cost of Samantha's 15th birthday party depends on the number guest. The hall charges $250 for the use of the hall plus $12 p

Scorpion4ik [409]

Answer:

Equation: y=x(12)+250

Total cost: $550

3 0

2 years ago

Mrs. Stern washed

bekas [8.4K]

Answer:

Mrs. Stern washed more

$\frac{7}{20}$ laundry still needs to be washed.

Step-by-step explanation:

Total amount of laundry: $\frac{20}{20}$

$\frac{20}{20} -\frac{2}{5}-\frac{1}{4} =$

$\frac{20}{20} - \frac{8}{20} -\frac{5}{20} =$

$\frac{7}{20}$ of the laundry still needs to be done.

Mrs. Stern washed $\frac{8}{20}$ of the laundry.

Her son washed $\frac{5}{20}$ of the laundry.

Mrs. Stern washed more laundry than her son.

8 0

2 years ago

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50%50% of this population prefer

n200080 [17]

Answer:

0.1527

Step-by-step explanation:

Given that a researcher wishes to conduct a study of the color preferences of new car buyers.

Suppose that 50% of this population prefers the color red

15 buyers are randomly selected

Let X be the no of buyers who prefer red.

X has exactly two outcomes red or non red.

Also each buyer is independent of the other

Hence X is binomial with p = 0.5 and n = 15

Required prob =The probability that exactly three-fifths of the buyers would prefer red

= P(X=9)

= $15C9 (0.9)^9 (0.6)^6$

= $5005(0.0000305)=0.1527$

6 0

2 years ago

The legs of an isosceles right triangle are 11 cm long. Find the length of the hypotenuse. Round to the nearest tenth if necessa

GaryK [48]

Its a squared + xb squared = c squared so its 11 squared + 11 squared equals c squared. So I'm gonna take it down to the next step and say 11x11+ 11x11= c squared, then you end up with 121+121= c squared then you add those two and end up with 242= c squared, so then you find the square root of 242 so you should end up with 15.5 and the number goes on and on and on

7 0

2 years ago