Solve the system of equations algebraically. Verify your answer using the graph. y = 4x – 5 y = –3

Answer:   [tex]\dfrac{27}{65}[/tex]

Step-by-step explanation:

There are 130 students.

There are 58 boys --> 72 girls

A) 49 chose football: 27 are girls --> 22 are boys

B) 72 girls: 24 chose running, 27 chose football --> 21 girls chose tennis

C) 27 students chose tennis: 21 are girls --> 6 are boys.

D) 58 boys: 22 chose football, 6 chose tennis --> 30 boys chose running.

[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&22&27&49\\Tennis&6&21&27\\\underline{Running}&\underline{\quad 30\quad}&\underline{\quad 24\quad}&\underline{\quad 54\quad}\\Total&58&72&130\end{array}}[/tex]

Total running = 30 boys + 24 girls = 54

Total students = 130

[tex]\dfrac{\text{Total running}}{\text{Total students}}=\dfrac{54}{130}\quad \rightarrow \large\boxed{\dfrac{27}{65}}[/tex]

Answer: B

Step-by-step explanation:

Quadratic parent function is y=x^2  which means the vertex is the origin because if you input 0 into the function you will get an output of zero. (0,0) is the origin which is where the graph intersect.

Answer:

Part A: check B, E and F.

Part B: check E and G.

Step-by-step explanation:

The equation [tex]y = a(x - b)^2 + c[/tex] is the equation of a parabola written in the vertex form, where the vertex will be (b, c).

So, if the vertex is (2, -1), we have that b = 2 and c = -1

To find the c value, we use the information that the y-intercept is 3, so we have the point (0, 3). Using x = 0 and y = 3, we have:

[tex]3 = a(0 - 2)^2 - 1[/tex]

[tex]3 = 4a - 1[/tex]

[tex]4a = 4[/tex]

[tex]a = 1[/tex]

So we have a = 1, b = 2 and c = -1.

Part A: check B, E and F.

To find the x-intercepts, we need to find the values of x where y = 0:

[tex]0 = (x - 2)^2 - 1[/tex]

[tex]x^2 - 4x + 4 - 1 = 0[/tex]

[tex]x^2 - 4x + 3 = 0[/tex]

Solving using Bhaskara's formula (a = 1, b = -4 and c = 3), we have:

[tex]\Delta = b^2 - 4ac = 16 - 12 = 4[/tex]

[tex]x_1 = (-b + \sqrt{\Delta})/2a = (4 + 2)/2 = 3[/tex]

[tex]x_2 = (-b - \sqrt{\Delta})/2a = (4 - 2)/2 = 1[/tex]

So the x-intercepts are 1 and 3

Part B: check E and G.

Answer:

1) 24Z^2 - 177.

2) 16d^2 - 32d.

6) 30x - 24.

7) 6q - 4.

Step-by-step explanation:

1) 3(8Z^2 - 52 - 7)

= 3(8Z^2 - 59)

= 24Z^2 - 177

2) 8d(2d - 4)

= (8d * 2d) - (8d * 4)

= 16d^2 - 32d

6) 6(5x - 4)

= (6 * 5x) - (6 * 4)

= 30x - 24

7) Already simplified. 6q - 4.

Hope this helps!

Answer:

20=6?

Step-by-step explanation:

14-2+8=2*3

14-2+8=6

12+8=6

20=6?

Answer:

These to equations aren't equivalent.

Step-by-step explanation:

14-2+8=2*3

12+8=6

20=6

Hope this helps ;) ❤❤❤

Explanation:

We'll use the tangent ratio to connect the opposite and adjacent sides with the reference angle

tan(angle) = opposite/adjacent

tan(A) = 14/7

Then use the arctangent function (aka inverse tangent) to fully isolate A

A = arctan(14/7)

A = 63.4349 degrees approximately; make sure your calculator is in degree mode

Round this to the nearest whole number to get 63.

Answer: square 105

Step-by-step explanation: Confirming answer

A radical expression is an expression containing a square root, mostly a square root.

The value of √3.√5.√7 in radical form is √105.

A radical expression is an expression containing a square root, mostly a square root.

We have,

√3.√5.√7

We can multiply the numbers together.

= √(3 x 5 x 7 )

= √(15 x 7)

= √105

Thus the value of √3.√5.√7 in radical form is  √105.

Learn more about radical form here:

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Answer:

Step-by-step explanation:

f(x) = 3x + 2

To find f(5) substitute 5 into f(x)

That's

f(5) = 3(5) + 2

= 15 + 2

= 17

Hope this helps you

Answer:

17

Step-by-step explanation:

You just plug 5 into the equation

f(5)= 3(5)+2

=15+2

=17

Hope this helped! :)

Answer:

Hey there!

This is an isosceles triangle, so if one angle is 44 degrees, (2 times 22), then the remaining angles add to 136 degrees.

136/2=68, so each of the angles are  68 degrees.

Hope this helps :)

Answer:

C = 68

Step-by-step explanation:

Y = 22

Then A = 2y = 2*22 = 44

We know that A + B + C = 180

And B = C since the base angles of an isosceles triangle are the same

44 + C+C = 180

44+2C = 180

2C = 180-44

2C =136

C = 68

Answer: d

Step-by-step explanation:

x*4=4x

5*4=20

Thus, all the new inequality is is a new, more complex version of the original.  Thus, the sign stays the same.

Hope it helps <3

Answer:

d)  ≥ .

Step-by-step explanation:

When x = 5 4x = 20.

hen x > 5  4x > 20.

Answer:

(-2,-3)

Step-by-step explanation:

abscissa is always know as the x axis

ordinate is known as y axis

therefore

it lies in the fourth quadrant

Answer:

in day 44 it covered half the area.

Step-by-step explanation:

A bacterial culture doubles every two days, so if today it covers [tex]3 cm^2[/tex], in two days it will cover [tex]6cm^2[/tex]. In other words, if today it covered x space, two days ago it covered half the space [tex](\frac{x}{2})[/tex].

Now, following that reasoning, we have that after 46 days the bacterial culture covered the entire surface area in the Petri dish, therefore, two days ago it covered half the area and we can conclude that in day 44 it covered half the area.

Answer:

You are m + 1 years old.

Step-by-step explanation:

Let's say that you are x years old, and Mack is m years old.

x = 1/2( two plus twice m)

x = 1/2(2 + 2m)

x = 1 + m

x = m + 1

Hope this helps!

Answer:

(-1,0), (0,3) and (2,2.25)

Step-by-step explanation:

The qualitative graph is as follows:

A(-1,0) ------> B(0,3) ------> C(2,2.25)

Hence, slope = (2.25 - 0)/(2 - (-1)) = 2.25/3

∴ slope = 0.75

Except for the option graph on a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), all the graph is qualitative. Options B, C, and D are correct.

The kind of graph that shows the quality curve such as decreasing and increasing events, is called a qualitative graph or curve.

Here,
1. On a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), since this graph does not represent any data as well as also constantly increasing between two points so it is not a qualitative graph.

Similarly,
Graphs B, C, and D have an increasing and decreasing order, so all are qualitative graphs.

Thus, except for graph A all the graphs are qualitative graphs.

Learn more about qualitative graphs here:
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Answer:

x=3 y=11

Step-by-step explanation:

2x+3=9

2x=6

x=3

y-4=7

y=11

Answer:

first option

Step-by-step explanation:

Given

- 3x - 2y = 1 → (1)

- x + y = 3 → (2)

Rearrange (2) by adding x to both sides, that is

y = x + 3

Substitute y = x + 3 into (1)

- 3x - 2(x + 3) = 1 ← is the equation to be solved for x

Answer:

[tex]\large\boxed{\sf \ \ 49 \ \ }[/tex]

Step-by-step explanation:

Hello,

we need to get the discriminant = 0 meaning

[tex]\Delta = b^2-4ac = 0\\\\<=>14^2-4c=0\\\\<=>c=\dfrac{196}{4}=49[/tex]

And then the square is

[tex]x^2-2\cdot 7\cdot x+7^2=(x-7)^2[/tex]

Hope this helps

Answer:

The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.

Answer:

The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.

Step-by-step explanation:

Hey Mate!!

Your answer will be below.

Step-by-step explanation:

The answer is C. Because, There's vertical asymptotes at 1 and -1. Vertical asymptotes are present where the x on the denominator is equal to 0. So, Both the values are 1 and -1 set are equal to the 0 in the denominator, So, They're both horizontal asymptotes. Good Luck!

Answer:

The volume is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{ 3} [/tex]

where r is the radius

π = 3.14

From the question we were given the diameter and

radius = diameter/ 2

diameter = 2 feet

radius = 2/2 = 1 feet

So the volume of the sphere is

[tex]V = \frac{4}{3} (3.14)(1) ^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14[/tex]

V = 4.186

We have the final answer as

V = 4 ft³ to the nearest hundredth

Hope this helps you

Answer:

Step-by-step explanation:

Vertex of f is (-1, -4) so its range is limited to y≥-4

|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0

Answer:

D

Step-by-step explanation:

i just took the test

1) Identify the sample used in the study: B) The sample is the responses of the volunteers in the study

2)  What is the​ sample's population: B) The population is collected of the response of all individuals who completed the math test

3) Which part of the study represents the descriptive branch of​ statistics:

individuals who are not sleep deprived will be more likely to answer math questions correctly than individuals who are sleep deprived.

hope i helpd

-lvr

Answer:

x = 56 degrees

y = 62 degrees

Step-by-step explanation:

Given TS || PR

x = 56    ................. corresponding angles TS, PR parallel sides of trapezium.

VSK = x ...................... correspoinding angles given TU || SV

y = 118 - VSK          .......... given VSR = 118

= 118 - 56

= 62

Answer:

2x² + [tex]\frac{3}{2}[/tex] x - 5

Step-by-step explanation:

(f + g)(x) = f(x) + g(x), thus

f(x) + g(x)

= [tex]\frac{x}{2}[/tex] - 2 + 2x² + x - 3 ← collect like terms

= 2x² + [tex]\frac{3}{2}[/tex] x - 5

Answer:

<3 = 112 degrees

<4 = 68 degrees

Step-by-step explanation:

<3 = 112 degrees (Alternate angles are congruent)

And,

<4+<3 = 180 (Angles on a straight line add up to 180)

=> <4 + 112 = 180

=> <4 = 180-112

=> <4 = 68 degrees

Answer:

CE = 100°

Step-by-step explanation:

Using the cofunction identity

sin x = cos(90 - x)

Given x = 20°, then 90° - 20° = 70° thus

CE - 30 = 70° ( add 30 to both sides )

CE = 100°

Thus

sin20° = cos(100 - 30)° = cos70°

Answer:

CE = 100

have a nice day!

Step-by-step explanation:

===============================================

Explanation:

Use the distance formula to get this answer. The idea is you subtract the x coordinates together, and do the same for the y coordinates as well. Square each result and add up those squares. The last step of the formula is to apply the square root to get the distance from A to B, which is also the length of segment AB.

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-3-5)^2+(-2-(-4))^2}\\\\d = \sqrt{(-3-5)^2+(-2+4)^2}\\\\d = \sqrt{(-8)^2+(2)^2}\\\\d = \sqrt{64+4}\\\\d = \sqrt{68}\\\\[/tex]

Therefore, [tex]AB = \sqrt{68}[/tex]

Answer:53 dresses

Step-by-step explanation:

First of all..if one kid required 2 1/4m of cloth,what about 119 1/4m of cloth?

So u take 119 1/4m of cloth and divide it by 2 1/4m of cloth.

Then change the mixed numbers into improper fractions.

So the question will be 477/4 m divided by 9/4 m.

The second improper fraction (9/4)m will be reciprocated to be (4/9)m.

Afterwards,take 477/4 m and multiply it by 4/9 m.

The result will be 53 dresses.