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guapka [62]
3 years ago
13

PLEASE HURRY! The price of a wallet is $32.95 and the sales tax is 7.5%. What is the total cost of the wallet?

Mathematics
1 answer:
Fiesta28 [93]3 years ago
3 0
\frac{7.5}{100} x 32.95 

=0.075 x 32.95 = $ 2.47 

The total cost of the wallet = price of the wallet + sales tax
                                           = 32.95 +  2.47
                                           = 35.42
Thus, the total cost of the wallet is $35.42
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Triangle ABC has vertices at A(2,3),B(-4,-3) and C(2,-3) find the coordinates of each point of concurrency.
dem82 [27]

Answer:

Circumcenter =(-1,0)

Orthocenter =(2,-3)

Step-by-step explanation:  

Given : Points A = (2,3), B = (-4,-3), C = (2,-3)  

Formula used :  

→Mid point of two points- (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

→Slope of two points - \frac{y_2-y_1}{x_2-x_1})

→Perpendicular of a line = \frac{-1}{slope of line})

Circumcenter- The point where the perpendicular bisectors of a triangle meets.

Orthocenter-The intersecting point for all the altitudes of the triangle.

To find out the circumcenter we have to solve any two bisector equations.

We solve for line AB and AC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = -1  

Equation of AB with slope -1 and the coordinates (-1,0) is,  

(y – 0) = -1(x – (-1))  

y+x=-1………………(1)  

Similarly, for AC  

Mid point of AC = (\frac{2+2}{2},\frac{3-3}{2})=(2,0)

Slope of AC = \frac{-3-3}{2-2}=\frac{-6}{0}  

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = 0  

Equation of AC with slope 0 and the coordinates (2,0) is,  

(y – 0) = 0(x – 2)  

y=0 ………………(2)  

By solving equation (1) and (2),  

put y=0 in equation (1)

y+x=-1

0+x=-1

⇒x=-1  

So the circumcenter(P)= (-1,0)

To find the orthocenter we solve the intersections of altitudes.

We solve for line AB and BC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of CF = -1  

Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF  

(y – 0) = -1(x – (-1))  

y+x=-1………………(3)  

Similarly, mid point of BC =(\frac{-4+2}{2},\frac{-3-3}{2})=(-1,-3)

Slope of AB =\frac{-3+3}{-4-2}=0

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of AD = 0

Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD

(y-(-3)) = 0(x – (-1))  

y+3=0

y=-3………………(4)  

Solve equation (3) and (4),

Put y=-3 in equation (3)

y+x=-1

-3+x=-1

x=2

Therefore, orthocenter(O)= (2,-3)


7 0
3 years ago
The radius of a circle measures 12 centimeters.<br> What is the circumference of the circle?
Travka [436]

Answer:

C=24π

Step-by-step explanation:

C=2πr

C=2π12

C=24π

≈75.39

8 0
2 years ago
Which equation is made true by the opposite angles theorem?
Oksana_A [137]

Solution

Step 1

The opposite angles of a parallelogram are equal:

Step 2

85\text{ + y  =  3y - 15}

The equation is made true by the opposite angles theorem is

85 + y = 3y - 15

or

y = 50

4 0
1 year ago
Find the midpoint of the segment with the given endpoints . G(-3,-5) and H(1,-1)
Serhud [2]
All you have to do for this is follow the midpoint formula.

Let me know if the picture is unclear and I'll type it out for you.

4 0
2 years ago
How many even 5-digit numbers can be formed from the numbers 1, 2, 4, 7, 8 if no digit is repeated in a number? A. 72 B. 120 C.
katovenus [111]
Hello,

Let's place the last digit: it must be 2 or 4 or 8 (3 possibilities)

It remainds 4 digits and the number of permutations fo 4 numbers is 4!=4*3*2*1=24

Thus there are 3*24=72 possibilities.

Answer A

If you do'nt believe run this programm

DIM n(5) AS INTEGER, i1 AS INTEGER, i2 AS INTEGER, i3 AS INTEGER, i4 AS INTEGER, i5 AS INTEGER, nb AS LONG, tot AS LONG
tot = 0
n(1) = 1
n(2) = 2
n(3) = 4
n(4) = 7
n(5) = 8
FOR i1 = 1 TO 5
    FOR i2 = 1 TO 5
        IF i2 <> i1 THEN
            FOR i3 = 1 TO 5
                IF i3 <> i2 AND i3 <> i1 THEN
                    FOR i4 = 1 TO 5
                        IF i4 <> i3 AND i4 <> i2 AND i4 <> i1 THEN
                            FOR i5 = 1 TO 5
                                IF i5 <> i4 AND i5 <> i3 AND i5 <> i2 AND i5 <> i1 THEN
                                    nb = ((((n(i1) * 10) + n(i2)) * 10 + n(i3)) * 10 + n(i4)) * 10 + n(i5)
                                    IF nb MOD 2 = 0 THEN
                                        tot = tot + 1
                                    END IF
                                END IF
                            NEXT i5
                        END IF
                    NEXT i4
                END IF
            NEXT i3
        END IF
    NEXT i2
NEXT i1
PRINT "tot="; tot
END


7 0
3 years ago
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