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allochka39001 [22]

3 years ago

6

Franco says that when he multiplies any number by a factor, the product is always equal to the number. What is the factor? Expla

in how you know this is true.

1 answer:

olya-2409 [2.1K]3 years ago

8 0

1 because any number times 1 equals itself.

Example: 3 times 1 = 3

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It took Leo 3 hours to type a 4125-word essay. Sarah typed her 3800-word essay in 3 hours and 10 minutes. At these rates, how mu

scoray [572]

Answer:

Sarah would take 35 minutes longer than Leo to type 5500 word essay

Step-by-step explanation:

Let us solve the question

∵ It took Leo 3 hours to type a 4125-word essay

→ The rate is the number of words divided by the time

∴ Leo's rate = 4125 ÷ 3 = 1375 words/hour

∵ Sarah typed her 3800-word essay in 3 hours and 10 minutes

→ Change the 10 min to the hour by divide it by 60

∵ 3 hours 10 min = 3 + $\frac{10}{60}$ = 3 + $\frac{1}{6}$ = 3 $\frac{1}{6}$ hours

∴ Sarah's rate = 3800 ÷ 3 $\frac{1}{6}$ = 1200 words/hour

∵ Leo will type a 5500-word essay

→ Divide it by his rate to find the time taken

∴ Leo takes = 5500 ÷ 1375 = 4 hours

∵ Sarah will type a 5500-word essay

→ Divide it by her rate to find the time taken

∴ Sarah takes = 5500 ÷ 1200 = 4 $\frac{7}{12}$ hours

→ Find the difference between their times

∵ The difference = 4 $\frac{7}{12}$ - 4 = $\frac{7}{12}$ hour

→ Multiply it by 60 to change to minutes

∴ The difference = $\frac{7}{12}$ × 60 = 35 minutes

∴ Sarah would take 35 minutes longer than Leo to type 5500 word essay

3 0

3 years ago

Write an equation of the line, in standard form, containing the points (−6, 19) and (−15, 28).

Rudiy27

The equation of the line that contains (−6, 19) and (−15, 28), in standard form, is: x + y = 13

<em><u>Recall:</u></em>

Equation of a line can be written in standard from as Ax + By = C, where Ax and By are all terms of variable x and y, and C is a constant.

The equation of a line in point-slope, $y - y_1 = m(x - x_1)$ , can be rewritten in the standard form.

Slope (m) = $\frac{y_2 - y_1}{x_2 - x_1}$

Given: (−6, 19) and (−15, 28)

<em>Find the </em><em>slope </em><em>(m):</em>

<em /> $m = \frac{28 - 19}{-15 -(-6)} = \frac{9}{-9} = -1$

Write the equation in point-slope form by substituting m = -1 and $(x_1, y_1) = (-6, 19)$ into $y - y_1 = m(x - x_1)$ .

$y - 19 = -1(x - (-6))\\\\y - 19 = -1(x + 6)$

Rewrite in standard form

$y - 19 = -1(x + 6)\\\\y - 19 = -x - 6\\\\y = -x - 6 + 19\\\\y = -x + 13\\\\\mathbf{x + y = 13}$

Therefore, the equation of the line that contains (−6, 19) and (−15, 28), in standard form, is: x + y = 13

Learn more about equation of a line in standard form on:

brainly.com/question/19169731

7 0

2 years ago

a car with a 20 gallon gas tank can go 25 miles on 1 gallon of gas. if the tank is full at the begining of the trip, how many ti

Tom [10]

37 times 720 divided by 20 is 36 then you need gas to run the 5 other miles.

6 0

3 years ago

WHO DOESN'T LOVE MAX POINTS. MAX POINT QUESTION<br> PLS ANSWER THIS TRIGONOMETRY QUESTION

mezya [45]

Answer:

Solution given:

opposite:9

adjacent: 12

$\theta=?$

Relationship between opposite and adjacent is given by tan angle

so

$Tan \theta=\frac{opposite} {adjacent}=\frac{9}{12}$

$Tan \theta=\frac{3}{4}$

$\theta=Tan^{-1}\frac{3}{4}$

$\bold{\theta=36.8°}$

#11.

hypotenuse[h]=11cm

opposite/perpendicular[P]=b cm

adjacent/base[b]=a cm

now

$\theta=62°$

Relationship between height and hypotenuse is given by Sin angle

:.

Sin 62°= $\frac{opposite}{hypotenuse}=\frac{b}{11}$

doing crisscrossed multiplication

b=Sin 62°*11

:.b=9.71 cm

a) At <u>9</u><u>.</u><u>7</u><u>1</u><u> </u>cm height does the ladder touch the building.

again

Relationship between base and hypotenuse is given by Cos angle

:.Cos 62°= $\frac{base}{hypotenuse}=\frac{a}{11}$

doing crisscrossed multiplication

a=Cos 62°×11

a=5.16cm

b) the distance between the foot of the ladder and the building is <u>5.16cm.</u>

4 0

2 years ago

Using the proportion 2/5=y/100 which equation can be used to find the value of Y

natulia [17]

2/5 = y/100
40/100 = y/100
Y=40

4 0

3 years ago