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Katena32 [7]
3 years ago
5

Evaluate the following expression, 5x [7+ (10-2) + 4)

Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0

Answer: 95x

Step-by-step explanation: Remove parentheses. 5x(7+10-2+4)

Add 7 and 10.

5x(17-2+4)

Add 15 and 4.

5x multiped by 19

Multiply 19 by 5

95x

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The sun shines at a 30° angle to the ground. To the nearest inch, how long is the shadow cast by a 72-in. tall fence post?
tensa zangetsu [6.8K]

The length of the shadow is 124.7 in

<u>Explanation:</u>

<u />

Given:

Angle, θ = 30°

Height of the fence,  h = 72 in

Length of the shadow, l = ?

Given:

tan 30° = \frac{perpendicular}{base}  = \frac{height of the fence}{length of the shadow}

\frac{1}{\sqrt{3} } = \frac{72}{l} \\\\l = 72\sqrt{3} \\\\l = 124.7 in

Therefore, the length of the shadow is 124.7 in

5 0
3 years ago
Becky needs to put 4 cups of flour into her bread maker to make one loaf of bread. She is using a measuring cup that holds 13 cu
pav-90 [236]

Answer:

12

Step-by-step explanation:

From the above question, we ate told that:

Becky needs to put 4 cups of flour into her bread maker to make one loaf of bread.

The size of her measuring cup = 1/3 cup

The number of 1/3 cups of flour she will need to make a loaf of bread is calculated as:

4 cups of flour ÷ 1/3 cup of flour

= 4 cups of flour × 3/1 cup of flour

= 12

4 0
2 years ago
Which of the following absolute value equations has no solutions?Group of answer choices
Amiraneli [1.4K]

The absolute value measures the distance a number is away from the origin (zero) on the number line. A number can be to the left or right of zero on the number line, but the distance away from zero is always positive. Graphically:

In other words:

• If d is positive and

\begin{gathered} |x|=d \\ \text{ then} \\ x=d\text{ or }x=-d \end{gathered}

• If d is negative and

\begin{gathered} |x|=-d \\ \text{then} \\ \text{ No solution, because distance (d) can not be negative.} \end{gathered}

Therefore, the equation that has no solutions is:

\boldsymbol{|x|=-3}

3 0
1 year ago
Use the slope formula to determine the slope of the line.
lukranit [14]

Answer:

we have two points

(0,4) and (3,-1)

m=(-1-4)/(3-0)

m=-5/3

5 0
3 years ago
Use the Law of Cosines to find angle round to the nearest tenth if necessary).
ad-work [718]

Answer:

Step-by-step explanation:

3a)

find side HP  , let's set side HP = c in the law of cosines formula

then

c = sq rt [ 23^2 + 12^2 - 2*12*23*cos(117) ]

c = sq rt [ 529 + 144 - (-250.6027559) ]

c = sq rt [ 673 + 250.6027559 ]

c = sq rt [ 923.602755 ]

c = 30.39

then

HP = 30.4  ( rounded to nearest 10th )

3b)

let PR = c, then law of cosines is (we need angle Q also 180=24+97+Q is 59°

c = sq rt [ 9^2 + 22^2 - 2*9*22*cos(59) ]

c = sq rt [ 81 + 484 -396*0.5150380 ]

c = sq rt [ 565 - 203.955 ]

c = sq rt [ 391.04495]

c = 19.7748

PR = 19.8  ( rounded to nearest 10th )

3c)

they want us to find ∠B,   in the formula for cosines ∠B is really ∠C, it's a bit confusing.. I'm sure they did that on purpose to mess people up.  Kind of underhanded  :/    Tell the teacher that you're "appalled" at the deviousness of the test  :/   stage a protest against math that teaches treachery  :P  storm the principals/ dean's  office with paper airplanes and pictures of anime   :DDD  okay back to math.

a=28

b=17

c=15

since we want angle B then the formula looks like

B= arcCos ( a^2 + c^2 - b^2 / 2*a*c)  so we'll avoid messing up the which side is which ... by setting up the formula this way   .. got it?

B = arcCos [28^2 + 15^2 - 17^2 / 2*28*15]

B = arcCos[784 + 225 - 289 /840 ]

B = arcCos[720/ 840]

B = arcCos[0.85714285]

B = 31.0027 °

that it came out so close to an integer I'm pretty sure it's right

∠B = 31 .0 °  ( rounded to the nearest 10th )

3d)

find ∠A

set it up carefully again, they are asking us to move the variable around again

a = 18

b= 28

c= 12

then the formula looks like

∠A = arcCos[ b^2 + c^23 - a^2 / 2*b*c ]

∠A = arcCos[28^2 + 12^2 - 18^2 /2*28*12 ]

∠A = arcCos[784 + 144 -324 / 672 ]

∠A = arcCos[604/672]

∠A = arcCos[0.8988095]

∠A =25.99797 °

∠A =26.0 °  ( rounded to nearest 10th)

7 0
3 years ago
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