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3 years ago

The line 2x + 3y = -6 intersects the x axis at (a,0) and the y axis at (0,b) what is a + b ?

1 answer:

3 0

2x + 3y = -6 (Subtract 2x from both sides)
3y = -2x - 6 (Divide both sides by 3 to isolate x) which will give you y = -2/3x - 2 and this graphed would cross the x-axis at (-3,0) and the y-axis at (0, -2). So a + b = -5

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Simplify.

pantera1 [17]

-12 + 9 - (-3) - 11

Remember PEMDAS: This is the order of operation.
P-Paragrahp
E-Exponent
M-Multiply
D-Divide
A-Add
S-Subtract

1st step: PEM
-(-3) is actually -1 * -3 = + 3

-12 + 9 + 3 - 11

2nd step: D is not possible, so we do A.
9 + 3 = 12

3rd Step: Subtract
12 - 12 - 11 = 0 - 11 = -11 CHOICE B.

7 0

3 years ago

A custom rectangular tabletop has a length that is twice it’s width, and the tabletop measures 76 inches on its diagonal. What a

Sunny_sXe [5.5K]

Answer:

<em>The dimensions of the tabletop: Length= 67.976... inches and Width= 33.988... inches and the perimeter will be 203.929... inches.</em>

Step-by-step explanation:

Suppose, the width of the rectangular tabletop is $x$ inch.

As the tabletop has a length that is twice it’s width, so the length will be: $2x$ inch.

The tabletop measures 76 inches on its diagonal.

<u>Formula for length of diagonal of rectangle</u>: $d=\sqrt{l^2+w^2}$

So, the equation will be..........

$76=\sqrt{(2x)^2+ x^2}\\ \\ 76=\sqrt{4x^2+x^2} \\ \\ 76=\sqrt{5x^2} \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= \frac{5776}{5}=1155.2 \\ \\ x= \sqrt{1155.2} =33.988...$

Thus, the width of the tabletop is 33.988... inches and the length will be: (2×33.988...) = 67.976... inches.

The perimeter will be: 2(33.988...+ 67.976...) inches = 203.929... inches.

5 0

3 years ago

Find the slope of line that passes through the points (4,-6) and (7,2)

BartSMP [9]

Answer:

8/3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

(03.03 MC)

notsponge [240]

Answer:

The slope of f(x) is 10 and the slope of g(x) is 5; g(x) has the greater y-intercept.

To find the slope of f(x), we use the slope formula: m=(y₂-y₁)/(x₂-x₁) = (-1--11)/(0--1) = (-1+11)/(0+1) = 10/1 = 10.

To find the slope of g(x), we just look at the form it is in. It is written in slope-intercept form, y=mx+b, where m is the slope. The number in g(x) that would correspond to m is 5.

The y-intercept of f(x) is found by looking at the points. Any y-intercept will have an x-coordinate of 0; the only point like this in the table is (0, -1) so the y-intercept is -1.

For g(x), we again look at the form y=mx+b. The number that corresponds with b is the y-intercept; in this case, it is 1. 1>-1, so g(x) has the larger y-intercept.

4 0

2 years ago

The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and 16.

Ostrovityanka [42]

Answer:

a) $\bar X = 121.4$

b) $SE = \frac{\sigma}{\sqrt{n}}= \frac{15}{\sqrt{40}}=2.372$

c) $121.4-1.64\frac{15}{\sqrt{40}}=117.51$

$121.4+1.64\frac{15}{\sqrt{40}}=125.29$

Step-by-step explanation:

Data given: 126,111,141,96,123,115,116,113,127,114,122,116,104,126,126,132,139,111,143,121,119,107,154,125,120,135,142,132,94,103,143,115,132,107,118,105,101,135,94,153

Part a

For this case we can calculate the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And after replace we got:

$\bar X = 121.4$

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

For this case we assume that the population deviation is $\sigma=15$ , we can calculate the standard error with this formula:

$SE = \frac{\sigma}{\sqrt{n}}= \frac{15}{\sqrt{40}}=2.372$

Part c

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$121.4-1.64\frac{15}{\sqrt{40}}=117.51$

$121.4+1.64\frac{15}{\sqrt{40}}=125.29$

8 0

3 years ago

Read 2 more answers