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4 years ago

The sum of two numbers is 27. One number is seven less than the other. Find the numbers

Mathematics

1 answer:

Marat540 [252]4 years ago

6 0

Answer:

17 and 10

Step-by-step explanation:

Write the problem as an equation.

a+b=27

a=b-7

Where a and b are the two numbers you are trying to find. You could use any variables. Then solve.

b+(b-7)=27 Sub (b-7) for a

2b-7=27 Group like terms

2b=34 Add 7 to both sides

b=17 Divide both sides by 2.

Because b=17, a must be 10.

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Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch. She slipped and spilled 1/4 of t

sasho [114]

Answer:

Susan spilled 1/6 of a gallon of lemonade.

Step-by-step explanation:

Since Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch, and she slipped and spilled 1/4 of the lemonade in the pitcher, to determine what fraction of a gallon of lemonade did she spill the following calculation must be performed:

2/3 = 0.6666

0.666666 x 1/4 = X

0.166666 = X

0.166666 = 1/6

Therefore, Susan spilled 1/6 of a gallon of lemonade.

3 0

3 years ago

If 1 lb. of strawberries cost 2.75, how much is 6 lbs.?

Snezhnost [94]

Answer:

$16.5

Step-by-step explanation:

if one pound is 2.75 dollars (unit rate) you multiply 2.75 by six to get the cost of six pounds.

6 0

2 years ago

Read 2 more answers

The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable

klemol [59]

Answer:

a) $y=0.75 x -10.65$

b) $y= 0.749*113 - 10.652=73.985\ approx 74.0$

Step-by-step explanation:

We assume that the data is this one:

x: 150 129 142 112 134 122 126 120

y: 88 96 106 80 98 63 95 64

Part a

We want to find a linear model $y = mx+b$ . Where:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =1035$

$\sum_{i=1}^n y_i =690$

$\sum_{i=1}^n x^2_i =134965$

$\sum_{i=1}^n y^2_i =61290$

$\sum_{i=1}^n x_i y_i =90064$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=134965-\frac{1035^2}{8}=1061.875$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=90064-\frac{1035*690}{8}=795.25$

And the slope would be:

$m=\frac{795.25}{1061.875}=0.749$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{1035}{8}=129.375$

$\bar y= \frac{\sum y_i}{n}=\frac{690}{8}=86.25$

And we can find the intercept using this:

$b=\bar y -m \bar x=86.25-(0.749*129.375)=-10.652$

So the line would be given by:

$y=0.75 x -10.65$

Part b

For this case w ejust need to replace x= 113 in the regression model and we got this:

$y= 0.749*113 - 10.652=73.985\ approx 74.0$

4 0

4 years ago

An angle, θ, is in standard position. The terminal side of the angle passes through the point (4, 5).

lara31 [8.8K]

Answer:

cos Θ = $\frac{4}{\sqrt{41} }$

Step-by-step explanation:

Given the angle passes through (4, 5 ) then the right triangle with sides 4 and 5 has hypotenuse h given by

h² = 4² + 5² = 16 + 25 = 41 ( take the square root of both sides )

h = $\sqrt{41}$

In relation to Θ, 4 is adjacent and 5 is opposite, thus

cos Θ = $\frac{adjacent}{hypotenuse}$ = $\frac{4}{\sqrt{41} }$

5 0

3 years ago

2x-3=-6x+12<br><br> Es para hoyyyy

Svet_ta [14]

Answer:

Step-by-step explanation:

2 x -3 = -6

-6 + 12 = -6 + -6 + 6

-6 + 12 = 6

8 0

3 years ago