Jamal finds some dimes and quarters in his change purse. How much money (in dollars) does he have if he has 9 dimes and 4 quarters? How much money (in dollars) does he have if he has xx dimes and yy quarters?

Hi there!

[tex]\large\boxed{(-3, 8.25)}[/tex]

Solve for the vertex by completing the square:

y = -0.25x² - 1.5x + 6

Factor out a negative:

y = -(0.25x² + 1.5x) + 6

Remember that a square binomial is:

a² + 2ab + b²

We know that:

a² = 0.25, so a = 0.5

1.5 = 2ab, so:

1.5 = 2(0.5)b

b = 1.5

b² = 2.25

Thus:

y = -(0.25x² + 1.5x + 2.25) + 6 - (-2.25)

Simplify:

y = -(0.5x + 1.5)² + 8.25

Find the vertex by factoring out 0.5:

y = -0.5(x + 3)² + 8.25

Thus, the vertex is:

(-3, 8.25)

Answer:

x = 10.9

Step-by-step explanation:

Since this is a right triangle, we can us trig functions

tan theta = opp / adj

tan 54 = x / 7.9

7.9 tan 54 = x

x=10.87341

Rounding to the nearest tenth

x = 10.9

Answer: i would go with the third one

y = x^2 - 2x - 3

Factored Form: y = (x - 3)(x + 1)

X-Intercepts: (3, 0) and (-1, 0)

Axis of Symmetry: x = 1

Vertex: (1, -4)

Domain: All Real Numbers (or negative infinity to infinity)

Range: y > -4

Hope this helps!

Answer:

80 miles

Step-by-step explanation:

Please find attached the graph used in answering this question

On the graph, the distance travelled is on the vertical axis while the gallons consumed in on the horizontal axis

from the graph, the following can be deduced :

0 gallons is consumed when the car travels 0 mile

1 gallon is consumed when the car travels 30 miles

2 gallons is consumed when the car travels 60 miles

total mile travelled when the gallons consumed is : 2 2/3 x 30

8/3 x 30 = 80 miles

Answer:

Step-by-step explanation:

Table I

Given function is,

f(x) = [tex]b^x[/tex]

From the table attached,

For x = 0.827, value of function f(0.827) = 5,

f(0.827) = [tex]b^{0.827}[/tex]

Therefore, [tex]b^{0.827}=5[/tex]

[tex]\text{log}(b^{0.827})=\text{log}(5)[/tex]

0.827[log(b)] = log(5)

log(b) = 0.8452

b = [tex]10^{0.8452}[/tex]

b = 7

Therefore, function 'f' will be,

f(x) = [tex]7^x[/tex]

For f(x) = 9,

9 = [tex]7^x[/tex]

log(9) = log([tex]7^x[/tex])

log(9) = x[log(7)]

x = 1.129

Table II

Given function is g(x) = [tex]\text{log}_b(x)[/tex]

From the given table,

For x = 7, g(x) = 1

1 = [tex]\text{log}_b(7)[/tex]

[tex]b^1=7[/tex]

b = 7

Therefore, the function 'g' will be,

g(x) = [tex]\text{log}_7(x)[/tex]

For g(x) = 1.318

1.318 = [tex]\text{log}_7(x)[/tex]

[tex]x=7^{1.318}[/tex]

[tex]x=12.9968[/tex]

[tex]x=13.997[/tex]

Answer:

1st option

Step-by-step explanation:

3×2+5y=15

5y=15-6

y=9/5

Answered by GAUTHMATH

Answer:

19

Step-by-step explanation:

divide 76 by 4

Answer:

The third one

Step-by-step explanation:

Just took the quiz

Answer:m

Step-by-step explanation:m

Answer: 159

Step-by-step explanation:

We have to find the surface area of two triangles and 3 rectangles

To find the surface areas of the triangles, we use the formula: base x height / 2

6 x 5.5 / 2 = 16.5

Multiply that by 2 since there are 2 of them

16.5 x 2 = 33

To find the surface area of the rectangles, we multiply the length and width

7 x 6 = 42

Multiply that by 3 since there are 3 of them

42 x 3 = 126

Add up all the surface areas

126 + 33 = 159

Solution:-10

As <AGQ and <EQG are corresponding interior angles

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 60°+a=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow a=180-60[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow a=120}[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow b=75°}[/tex]

According to angle sum property

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow b+c+<PQR=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+75+60=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+135=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c=180-135[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow c=45°}[/tex]

Answer:

solution,

(X1,y1)= (-4,5)

(X2,Y2)=(2,-3)

slope of the line(m)= y2-y1/x2-x1

=-3-5/2-(-4)

=-8/6

=-4/3

c) y= -2x +1

Step-by-step explanation:

y= -2x +1

m= (- 3 -5)/2+2

= -2

c=1

y-(-3)= -2(x-2)

y= -2x +4 -3

y = -2x+1

Answer:

[tex]a. \ \dfrac{1}{36}[/tex]

[tex]b. \ \dfrac{4}{9}[/tex]

[tex]c. \ \dfrac{5}{6}[/tex]

Step-by-step explanation:

The given probabilities are; P(Orange) = 1/3, P(Blue) = 1/6, P(Purple) = 1/2

The probability of rolling any of the six numbers of the six-sided die = 1/6

a. The probability of simultaneously 'rolling a 3' and 'spinning blue', P(3 and Blue) is given as follows;

P(rolling a 3) = 1/6, P(Blue) = 1/6

∴ P(3 and Blue) = (1/6) × (1/6) = 1/36

P(3 and Blue) = 1/36

[tex]P(3 \ and \ Blue) = \dfrac{1}{36}[/tex]

b. The probability of either 'rolling a 1' or 'spinning Orange', P(1 or Orange), is given as follows;

P(rolling a 1) = 1/6, P(Orange) = 1/3

P(1 or Orange) = P(rolling a 1) + P(Orange) - P(1 and Orange)

Where;

P(1 and Orange) = (1/6) × (1/3) = 1/18

∴ P(1 or Orange) = 1/6 + 1/3 - 1/18 = 4/9

P(1 or Orange) = 4/9

[tex]P(1 \ or \ Orange) = \dfrac{4}{9}[/tex]

c. The probability of not spinning a blue, P(not Blue) is given as follows;

P(not Blue) = P(rolling all outcomes of the die) and (The sum of the spin probabilities - P(Blue)

∴ P(not Blue) = 1 × ((1/3 + 1/6 + 1/2) - 1/6) = 1 × (1 - 1/6) = 5/6

P(not Blue) = 5/6

[tex]P(not \ Blue) = \dfrac{5}{6}[/tex]

Answer:

1 ) 0.023

2 ) 0.1004

Step-by-step explanation:

2 / 100 + 3 / 1000

= 0.02 + 0.003

= 0.020 + 0.003

= 0.023

1 / 10 + 4 / 10,000

= 0.1 + 0.0004

= 0.1000 + 0.0004

= 0.1004

Answer:

The total value of quarters that Samantha took is $3.75

Step-by-step explanation:

Timothy has 72 coins.

He has:

Q quarters

D dimes

N nickels

8 pennies.

Then:

Q + D + N + 8 = 72

Samantha takes:

3 dimes

2 nickels

Leaves him with one penny, then she takes 7 pennies.

all of the quarters, so she took Q quarters.

So now Timothy has 45 coins.

And for each particular type of coin, Thimothy now has:

D - 3 dimes

0 quarters

1 penny

N - 2 nickels

And we know that he has 45 coins, then:

(N - 2) + 1 + ( D - 3) = 45

Which we can rewrite as:

N + D + 1 - 2 - 3 = 45

N + D - 4 = 45

N + D = 45 + 4 = 49

So we have two equations:

Q + D + N + 8 = 72

N + D = 49

Now we can replace the second equation into the first one:

(N + D) = 49

then:

Q + D + N + 8 = 72

Q + (D + N) + 8 = 72

Q + 49 + 8 = 72

Now we can solve this for Q

Q = 72 - 49 - 8 = 15

So Samantha took 15 quarters.

Each quarter has a value of $0.25

Then Samantha took:

15*$0.25 = $3.75

The total value of quarters that Samantha took is $3.75

Step-by-step explanation:

-23 is the answer

√18=9

√16=4

-3×9+4= -23

Answer:

-23 is right on edg

Step-by-step explanation:

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.

Step-by-step explanation:

There are mistakes in the statement, correct form is presented below:

[tex]5+\frac{\sqrt{3}}{7} + 2\sqrt{3} = a - b\cdot \sqrt{3}[/tex].

By direct comparison we have the following system of equations:

[tex]a = 5[/tex] (1)

[tex]\frac{\sqrt{3}}{7}+2\sqrt{3} = -b\cdot \sqrt{3}[/tex] (2)

In (2) we solve for [tex]b[/tex]:

[tex]\left(\frac{1}{7}+2 \right)\cdot \sqrt{3} = -b\cdot \sqrt{3}[/tex]

[tex]b = -\frac{15}{7}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.

Answer:

360 feets

Step-by-step explanation:

Given :

Scale : 1 inch = 12 feets

This means 1 inch on paper (model) represents 12 feets in real life

If the model height = 30 inches ;

The actual height of the Saturn V rocket will be :

1 inch = 12 feets

30 inch = x

x = (30 * 12)

x = 360 feets

Actual height = 360 feets

Your answer is attached above. hope it helps

if this value 35% less than the total, we conclude that:

42,900 = 65%

1% = 660

100% = 66,000

if you want to check the value, just do 65% of 66000, which equals to 42,900

hope it helps :)

Circumference of a circle = 2πr

So,

[tex]circumference = 2\pi \: r \\ = > circumference = 2 \times \frac{22}{7} \times \frac{63 \: cm}{2} \\ = > circumference = 2 \times \frac{11}{7} \times 63 \: cm \\ = > circumference = 2 \times 11 \times 9 \: cm \\ = > circumference = 198 \: cm[/tex]

Answer: Therefore, the circumference of circle is 198 cm.

Step-by-step explanation:

diameter = 63 cm

radius = 63/2 = 31.5 cm

circumference = ?

circumference or perimeter of circle = 2*pi*r

= 2*(22/7)*31.5

= (44/7)*31.5

= 198 cm

Point-slope form

y -24 = -4/5(x -0)

Find x when y is 0 (X-intercept)

0 -24 = -4/5(x -0)

-24 = -4/5x

x = -120/-4

x = 30

Answer: A. 30 minutes

Answer:

18 pages

Step-by-step explanation:

that means you can read 2 pages in 10 minutes.

an hour and a half is 90 minutes.

90 is 9 times more than 10.

so we do 2 * 9 = 18 pages

Answer:

14.88 km

Step-by-step explanation:

add both base 1 and base 2 together divide them by 2 then multiply by the height.